Project Description:
The present study investigates the distribution of sale prices for homes in a region in upstate New York. This project will also
seek to compare the distributions of sale prices between homes with central air and homes without central air. Suppose you are
being transferred to this area and are interested in getting a good description of selling prices for homes in this region. The
variables collected in the data are: Price: Recorded in dollars; Lot size: measured in acres; Living Area: measured in square
feet; Pct College: percent of students going to college; Central Air: No – 0, Yes – 1; Bedrooms: Number of bedrooms; Fireplace
Number of fireplaces; Bathrooms: Number of bathrooms. For the purpose of this project, you will only be using the variables
Instructions:
Use a cell reference or a single formula where appropriate in order to receive full credit. Do not copy and paste values or type
values, as you will not receive full credit for your answers. For the purpose of grading the project you are required to perform
the following tasks:
Step
1
2
3
4
5
6
7
8
9
10
11
12
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14
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17
Descriptive Numerical Analysis
roject Description:
he present study investigates the distribution of sale prices for homes in a region in upstate New York. This project will also
eek to compare the distributions of sale prices between homes with central air and homes without central air. Suppose you are
eing transferred to this area and are interested in getting a good description of selling prices for homes in this region. The
ariables collected in the data are: Price: Recorded in dollars; Lot size: measured in acres; Living Area: measured in square
eet; Pct College: percent of students going to college; Central Air: No – 0, Yes – 1; Bedrooms: Number of bedrooms; Fireplace:
umber of fireplaces; Bathrooms: Number of bathrooms. For the purpose of this project, you will only be using the variables
nstructions:
se a cell reference or a single formula where appropriate in order to receive full credit. Do not copy and paste values or type
alues, as you will not receive full credit for your answers. For the purpose of grading the project you are required to perform
he following tasks:
Instructions
Start Excel. Download and open the workbook named:
Descriptive_Numerical_Analysis_Start
Obtain the descriptive statistics for sale prices for all homes in the dataset.
Adding Descriptive Statistics
Go to the Data worksheet. Select Data Analysis in the Analysis group of the Data tab of the Ribbon (note you should add this
Add-in in case you do not have it in the Data tab already). Select Descriptive Statistics and click OK. Select the Price column as
the Input Range. Choose Grouped by Columns. Check the ‘Labels in the first row’ box. Choose cell I1 on the Data worksheet
In cell I16 on the Data worksheet, type Q1. In cell J16, calculate the value of the first quartile for the Price data set.
In cell I17 on the Data worksheet, type Q3. In cell J17, calculate the value of the third quartile for the Price data set.
In cells D7-D14 on the Problem worksheet, identify the values for the mean, standard deviation, minimum, first quartile,
median, third quartile, maximum, and sample size. Round the monetary values to the nearest cent.
In cell D18, identify the range of sales prices.
In cell D19, calculate the size of the bins for 25 bins.
To construct the histogram, first create a column of ‘bins’ on the Data worksheet. Since the bin size is not a round number in
thousands of dollars, choose the bin size to be 30,000. In cell K1 on the Data worksheet, type Binsize. In cell K2, type
Now construct the histogram.
Inserting the Histogram
On the Data worksheet, select Data Analysis in the Analysis group of the Data tab of the Ribbon. Select Histogram and click OK.
Select the Price column as the Input Range and the Binsize column (starting on cell K1) as the Bin Range. Check the ‘Labels’
box. Choose cell M1 on the Data worksheet as the output range. Check the ‘Chart Output’ box. Do not check any additional
Moving the Histogram
Select the Histogram. Then choose Move Chart in the Design tab on the Ribbon. Select the Problem worksheet in the provided
drop-down menu. Drag the histogram on the Problem worksheet and change its size so that it is located in cell C23.
Edit Chart
Change
theElements
title of the histogram to Distribution of selling prices. Right click on one of the bars and select ‘Format Data
Series’. Slide the ‘Gap Width’ to zero.
In cells F26-G26, choose how you would describe the shape of the distribution from the drop-down menu.
In cells F27-G27, choose which measure of 'center' is best to describe the distribution from the drop-down menu.
In cells F28-G28, choose how to compare the values of the mean and the median from the drop-down menu.
In cells F29-G29, choose which measure of 'spread' is best to describe the distribution from the drop-down menu.
In cell D34, calculate the percentage of homes rounded to one decimal place whose prices are expected to exceed $300,000
using the value(s) found in step 5.
In cell D36, calculate the percentage of homes rounded to one decimal place that are priced between $90,000 and $300,001,
exclusive, using the value(s) found in step 5.
In cell D38, calculate the percentage of homes rounded to one decimal place expected to be priced less than or equal to
$150,000 using the value(s) found in step 5.
Construct two histograms showing the distribution of prices for homes without central air and the prices for homes with central air.
First, create the two columns of data. On the Data worksheet, copy the Price column to columns P and Q. In cell P1, type
Price without central air. In cell Q1, type Price with central air. Then select the first row, go to the Home tab of the
Ribbon, and select Sort&Filter in the Editing group. Select Filter in the drop-down menu. In cell E1, open the drop-down menu
and select to show only value 0. Delete all of the filtered values in column Q. Then in cell E1 in the drop-down menu, select to
Construct the histogram using Data Analysis for the Price without central air column using the Binsize column K (starting on cell
K1). Choose cell R1 on the Data worksheet as the output range. Be sure to check the ‘Labels’ and ‘Chart Output’ boxes in the
Histogram menu. Move the histogram to the Problem worksheet and place it in cells B42-C42. Change the title of the
Construct the histogram using Data Analysis for the Price with central air column using the Binsize column K (starting on cell
K1). Choose cell T1 on the Data worksheet as the output range. Be sure to check the ‘Labels’ and ‘Chart Output’ boxes in the
Histogram menu. Move the histogram to the Problem worksheet and place it in cells D42-G42. Change the title of the
Obtain the descriptive statistics for sale prices for homes without central air. Go to the Data worksheet and use Descriptive
Statistics in Data Analysis for the Price without central air column. Choose cell V1 on the Data worksheet as the output range.
In cell V16 on the Data worksheet, type Q1. In cell W16, calculate the value of the first quartile for the Price without central
air
dataV17
set.on the Data worksheet, type Q3. In cell W17, calculate the value of the third quartile for the Price without central
In cell
air data set.
In cells E45-E51 on the Problem worksheet, identify the values for the minimum, first quartile, median, mean, third quartile,
maximum, and sample size. Round the monetary values to the nearest cent.
Obtain the descriptive statistics for sale prices for homes with central air. Go to the Data worksheet and use Descriptive
Statistics in Data Analysis for the Price with central air column. Choose cell X1 on the Data worksheet as the output range. Be
In
In cell
cell X16
X17 on
on the
the Data
Data worksheet,
worksheet, type
type Q1.
Q3. In
In cell
cell Y16,
Y17, calculate
calculate the
the value
value of
of the
the first
thirdquartile
quartilefor
forthe
thePrice
Pricewith
withcentral
centralair
airdata set.
data set.
In cells E45-E51 on the Problem worksheet, identify the values for the minimum, first quartile, median, mean, third quartile,
maximum, and sample size. Round the monetary values to the nearest cent.
In cells D55 and D56, compare the estimated sale prices of homes with central air to homes without central air. Choose the
correct answers from the drop-down menus.
In cell E58, calculate the expected difference in median costs. In cells D60, F60, D61, and F61, identify the variability of
prices using Q1 and Q3 for each data set. Use the descriptive statistics in cells D45-E51. Keep the same number of decimal
places as the values in step14 and step15.
Save the workbook. Close the workbook and then exit Excel. Submit the workbook as directed.
Total Score
Points Possible
0
8
1
1
4
1
1
1
1
1
1
1
8
7
7
7
0
50
Problem Housing Data
The present study investigates the distribution of sale prices for homes in a region in upstat
homes without central air. Suppose you are being transferred to this area and are interested
Use a cell reference or a single formula where appropriate in order to receive full credit. Do
1-2)
3)
4)
5)
6)
7)
8)
9)
10)
11)
12)
13)
14-15)
16)
Problem Housing Data
The present study investigates the distribution of sale prices for homes in a region in upstate New York an
homes without central air. Suppose you are being transferred to this area and are interested in getting a goo
Use a cell reference or a single formula where appropriate in order to receive full credit. Do not copy and p
Obtain the descriptive statistics for sale prices for all homes in the dataset. Provide the values below
Identify the mean sale price to the nearest cent in cell D7.
Identify the standard deviation of the sale prices to the nearest cent in D8.
Identify the minimum sale price to the nearest cent in cell D9.
Identify the first quartile sale price to the nearest cent in cell D10.
Identify the median sale price to the nearest cent in cell D11.
Identify the third quartile sale price to the nearest cent in cell D12.
Identify the maximum sale price to the nearest cent in cell D13.
Identify the sample size in cell D14.
To begin to construct the histogram of sale prices, we need to determine our bins. These are the upp
the prices, and dividing by the number of bars we want in our histogram. Since we have a large sam
Identify the range of sale prices in cell D18.
Calculate the size of the bins for 25 bins in cell D19.
Construct the histogram using the bins calculated. Follow the directions in step5 in the instructions
Describe the distribution of housing prices of homes in upstate New York.
In cells F26-G26, choose how you would describe the shape of the distribution from the drop-down
In cells F27-G27, choose which measure of 'center' is best to describe the distribution from the drop
In cells F28-G28, choose how to compare the values of the mean and the median from the drop-dow
In cells F29-G29, choose which measure of 'spread' is best to describe the distribution from the dro
Use the histogram (or the grouped frequency distribution) to answer the following.
In cell D34, calculate the percentage of homes rounded to one decimal place whose prices are expec
In cell D36, calculate the percentage of homes rounded to one decimal place that are priced between
In cell D38, calculate the percentage of homes rounded to one decimal place expected to be priced l
Suppose you are looking at two houses in the same neighborhood that are about the same size excep
Using the same bins you used in question 3), construct separate histograms for the sale prices for ho
histogram so that they are labeled appropriately by central air status. Insert the two histograms in ce
Obtain the descriptive statistics for sale prices for homes without central air and with central air in t
Minimum sale price, in cells D45 and E45
Q1, in cells D46 and E46
Median, in cells D47 and E47
Mean, in cells D48 and E48
Q3, in cells D49 and E49
Maximum, in cells D50 and E50
n, sample size, in cells D51 and E51
Write a brief summary statement comparing the sale prices of homes with and without central air us
expect to pay for 'typical' homes in this region of upstate New York using the statements provided b
In cells D55 and D56, compare the estimated sale prices of homes with central air to homes without
Homes with central air generally sell for
This is indicated by comparing the
Calculate the expected difference in median costs in cell E58. Keep the same number of decimal pla
Given this data, one would estimate that homes with central air can be expected t
Identify the variability of prices using Q1 and Q3 for each data set in cells D60, F60, D61, and F61
The variability of prices for the typical home without central air ranges from about
as compared to
pstate New York and to compare the distributions of sale prices between homes with central air and
sted in getting a good description of selling prices for homes there.
t. Do not copy and paste values or type values, as you will not receive full credit for your answers.
ide the values below:
s. These are the upper limits to the size of the bars on the x-axis. We do this by calculating the range of
we have a large sample size, let us choose to have about 25 bins.
in the instructions document. Insert the histogram in cell C23.
from the drop-down menu.
bution from the drop-down menu.
n from the drop-down menu.
bution from the drop-down menu.
ng.
ose prices are expected to exceed $300,000 using the value(s) found in step 5.
t are priced between $90,000 and $300,001, exclusive, using the value(s) found in step 5.
pected to be priced less than or equal to $150,000 using the value(s) found in step 5.
the same size except one of the homes has central air and the other one does not. Compare the
he sale prices for homes without central air and the sale prices for homes with central air. Title each
wo histograms in cells B42-G42.
with central air in the dataset. Provide the values below. Round the monetary values to the nearest cent.
Without Central Air With Central Air
ithout central air using the medians and the interquartile ranges as a general range of prices one would
atements provided below.
ir to homes without central air. Choose the correct answers from the drop-down menus.
prices than homes without central air.
home prices between homes with and without central air.
mber of decimal places as the values in step14 and step15.
ir can be expected to cost about
more than homes without central air.
F60, D61, and F61. Keep the same number of decimal places as the values in step14 and step15.
to
to
between homes with central air and
ere.
eceive full credit for your answers.
. We do this by calculating the range of
.
ound in step 5.
e value(s) found in step 5.
e(s) found in step 5.
ther one does not. Compare the
or homes with central air. Title each
d the monetary values to the nearest cent.
as a general range of prices one would
m the drop-down menus.
ith and without central air.
homes without central air.
s the values in step14 and step15.
for homes with central air.
Price
Lot Size
Living Area
Pct College
132500
0.09
906
181115
0.92
1953
109000
0.19
1944
155000
0.41
1944
86060
0.11
840
120000
0.68
1152
153000
0.4
2752
170000
1.21
1662
90000
0.83
1632
122900
1.94
1416
325000
2.29
2894
120000
0.92
1624
85860
8.97
704
97000
0.11
1383
127000
0.14
1300
89900
0
936
155000
0.13
1300
253750
2
2816
60000
0.21
924
87500
0.88
1092
112000
1
1056
104900
0.43
1600
148635
0.32
1576
150000
0.03
2080
90400
0.36
1600
248800
4
2224
135000
1.83
1656
145000
3
1170
457000
0.43
2461
140000
0.44
1544
130000
1.24
1220
187000
0.46
1858
229000
0.87
2219
227000
1.8
1876
179900
0.46
2026
169900
0.91
1671
209900
0.46
2060
169900
0.59
1884
293000
7.24
2022
245900
0.19
2394
157000
0.46
1390
195000
0.41
1954
150000
0.78
1554
234900
0.89
1976
279550
1.34
2479
246500
1
2714
Central Air
35
51
51
51
51
22
51
35
51
44
51
51
41
57
41
57
41
71
35
35
35
39
39
39
39
39
39
39
39
71
71
52
64
52
52
71
52
52
71
71
71
71
71
64
71
71
Bedrooms
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
1
1
0
0
Fireplaces
2
3
4
3
2
4
4
4
3
3
7
3
2
3
3
3
3
4
2
3
3
3
3
3
3
4
3
4
4
3
2
3
3
3
4
4
4
4
4
4
3
4
3
3
4
4
1
0
1
1
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
2
1
1
0
1
1
1
1
2
1
1
0
1
0
1
1
124000
138000
290000
108000
134900
64500
142000
125000
88000
135000
90000
90100
126900
175000
158000
92000
82800
140000
171000
200640
139000
225000
182000
208767
186000
93000
257386
161000
92000
211002
115000
113000
216300
145000
114000
139050
104000
169900
177900
133000
185000
115000
100000
117000
150000
187500
107000
1
0.27
0.71
0.9
0.24
0.06
0.55
0.34
0.19
0.23
0.07
0.09
0.25
0.47
0.36
0.07
0.11
0.23
3.16
0.08
0.57
0.5
1
0.5
0.55
0.1
0.5
0.31
0.28
0.06
0.06
0.46
0.1
2.12
0.06
0.21
0.06
0.26
0.29
1.29
1
0.88
0.52
0.07
0.32
0.92
0.46
797
1500
1838
1042
1782
1480
1426
1404
1480
1344
1480
1480
1596
1768
1348
1480
1483
1576
1008
2332
1064
2428
1310
1662
2000
1480
2969
1542
1527
2195
1480
1452
2360
1440
1480
1879
1480
1792
1386
1676
768
1560
1000
1676
1656
2300
1712
52
71
71
71
52
52
52
52
52
52
52
52
52
52
52
52
52
52
52
52
52
52
52
52
52
52
52
52
52
52
52
52
52
52
52
52
52
52
44
44
22
22
22
51
51
51
51
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
3
4
2
3
2
3
3
3
3
2
3
3
3
2
3
3
4
2
4
3
4
3
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4
3
4
3
4
4
3
3
4
3
2
3
3
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3
2
4
3
3
4
3
3
3
0
0
0
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1
1
0
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126900
147000
62000
101000
143500
113400
76320
110000
88000
108000
114900
146000
225000
138000
218070
25000
112000
112500
97000
121000
65720
225000
192000
158500
247000
193777
136500
75000
45000
243000
90000
158000
174000
150000
159650
139062
84950
102000
175000
78500
232478
93805
119900
146000
125000
135000
157500
0.46
0.11
0.4
0.87
0.59
0.93
0.15
0.59
0.33
0.32
0.46
0.48
2.37
0.83
1
0.21
0.27
0.72
0.36
0.52
0.19
0.38
0.82
0.69
0.51
0.72
0.62
1
0.52
0.82
0.29
0.52
0.64
0.52
1
0.69
0.13
0.22
0.46
1
1
0.13
1.03
1.17
0.34
0.38
1.96
1350
1676
1317
1056
912
1232
1380
936
720
1628
1144
1827
1784
1851
2194
920
1280
1232
1406
1164
1198
2206
1880
1368
1901
1547
896
1008
912
2443
900
2098
2115
1344
1106
1440
840
1170
1664
3024
2598
840
1701
1456
1224
1411
1608
51
51
51
51
51
44
44
44
44
44
44
44
44
44
44
44
44
44
44
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44
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51
51
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51
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41
41
71
71
71
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
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1
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3
3
3
3
3
2
3
3
3
2
3
3
3
3
4
2
3
3
3
3
3
4
3
3
3
3
3
3
2
3
4
3
4
2
3
3
2
2
4
4
4
2
5
3
3
3
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0
1
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0
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1
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1
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0
0
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0
0
0
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0
0
1
1
0
2
0
0
0
0
1
0
0
1
0
1
1
135000
142900
259900
85000
180377
163500
106500
115000
115000
135000
198900
139000
206000
120000
205980
275000
139000
89900
139900
172750
136000
270000
174000
379000
382500
144900
349900
133000
115000
211950
227812
164400
340000
139900
279900
225000
144500
362710
247000
120000
136000
228500
162800
230000
115800
175000
263008
3
0.33
0.46
0.29
0.35
0.28
0.52
0.11
0.14
0.14
0.47
0.14
0.51
0.21
0.14
0.55
0.07
0.49
0.07
0.36
0.5
0.48
0.29
0.68
4.08
0.1
0.62
0.07
0.16
0.36
0.01
0.34
0.75
0.29
0.47
0.32
0.12
1
0.46
0.18
0.55
0.46
0.15
0.93
0.46
0.26
0.63
3020
1898
2544
1038
1820
2202
2387
1368
1480
1348
1889
1343
2011
1180
1983
2253
1604
1196
1602
1747
1092
2410
1933
3080
4534
1677
2900
1392
1058
2342
2206
1516
2836
1256
2340
2129
1343
2963
2114
1144
988
1475
1247
1912
1440
1596
2665
41
64
64
64
64
64
64
64
64
64
64
64
64
64
64
64
64
45
64
64
64
64
64
64
64
64
64
64
64
64
64
64
64
64
64
64
64
64
64
64
64
64
64
64
64
64
64
0
0
1
0
0
1
0
1
1
1
1
1
1
1
1
1
1
0
1
0
0
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
0
0
0
0
0
1
1
4
3
4
2
3
3
3
2
2
2
4
2
3
2
3
3
2
3
2
3
3
4
3
4
6
3
4
2
2
4
4
3
4
2
4
4
2
4
4
2
3
3
3
5
3
3
4
0
1
1
0
1
1
0
1
1
1
1
1
1
1
1
1
0
0
0
0
0
1
1
1
2
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
0
0
1
0
1
1
146000
204900
265000
167500
205000
170000
176000
132000
115500
150000
120000
125000
150000
362360
133500
91000
104000
148000
182000
152500
97000
113000
172000
179900
84000
117900
177000
107500
92500
102900
134800
150000
165000
120000
177500
300000
123500
141000
105400
100600
108900
105500
109900
172700
166500
105000
490000
0.5
0.03
0.17
0.64
0.47
0.92
0.41
0.16
0.01
0.29
0.36
0.28
0.15
0.59
0.36
0.16
0.34
0.33
0.56
0.48
0.16
0.17
0.46
0.81
0.15
0.15
0.32
0.16
0.15
0.15
0.48
0.77
0.42
0.17
0.32
0.09
0.16
0.16
0.15
0.17
0.17
0.16
0.16
0.34
0.31
0.4
0.34
1984
1616
1917
2592
1845
1360
1664
1098
1214
1046
1144
1140
1232
3020
1508
912
1508
1561
2625
936
912
1492
1599
2304
912
1385
1561
884
912
912
1384
1334
1433
1492
1561
936
1492
1853
1240
912
912
912
1184
1638
1508
672
1346
64
64
64
64
64
57
64
64
64
57
64
64
64
64
52
52
52
52
64
52
52
52
64
52
52
52
52
52
52
52
52
52
64
52
52
52
52
52
52
52
52
52
52
52
52
52
52
0
1
0
0
0
1
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
3
3
3
3
4
3
2
2
3
3
2
2
4
3
2
3
3
4
3
2
3
4
5
2
2
4
2
2
2
3
3
3
3
4
1
3
3
2
2
2
2
3
3
3
2
3
0
0
1
1
1
0
1
1
0
0
0
1
1
1
1
1
0
1
1
1
0
0
1
1
0
1
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
1
1
0
1
120000
107500
116600
65000
118000
115900
100000
171000
188000
140000
124500
107200
107500
180000
214325
128850
208700
139900
350000
108000
115500
135000
135000
107400
233000
105000
335000
139000
209500
101000
77500
150500
167000
114000
160000
85000
143000
126000
140000
140000
205000
79900
139000
190000
151500
97500
194500
0.16
0.15
0.15
0.16
0.16
0.15
0.15
0.37
0.31
1
0.15
0.16
0.24
2.06
0.42
0.92
0.4
0.36
5.84
0.16
0.15
0.98
0.33
0.16
0.09
0.16
3
0.58
0.42
0.17
0.16
0.31
0.99
0.26
0.45
0.49
0.35
0.4
0.48
0.35
0.25
0.12
0.09
0.46
0.71
0.06
0.61
1184
912
912
988
1184
1385
912
1548
1561
1008
1385
908
2246
1820
2554
824
2458
1324
2916
1032
912
1320
1508
912
2040
912
1776
1304
1836
912
912
1527
1454
1700
1680
2401
1176
1344
1344
1714
1992
924
1290
2521
1377
1237
2310
52
52
52
52
52
52
52
52
52
52
52
52
39
39
64
45
64
64
64
52
52
52
52
52
52
52
52
64
64
52
52
52
39
39
45
64
64
64
64
64
64
64
64
64
82
64
64
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
1
3
2
2
2
3
2
2
3
4
2
2
2
4
3
4
3
4
3
3
2
2
2
3
2
4
2
2
3
4
2
2
2
3
3
4
4
3
3
3
3
4
2
2
4
3
2
4
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
1
0
1
0
1
1
1
1
0
0
1
0
0
1
0
1
0
1
0
1
0
0
1
0
1
1
1
1
1
195160
152500
159500
185000
240000
187900
262000
212500
220000
245000
120000
102500
136000
212500
205900
259900
191500
272500
191500
158000
195000
187500
160000
137500
109900
85000
184350
134500
154900
255000
238600
106000
625000
195000
168500
87000
215000
197500
215000
118000
187900
275000
249900
270000
157900
120000
126400
0.32
0.37
0.29
0.95
0.67
0.4
0.29
0.35
0.37
0.53
0.06
0.15
0.27
0.43
0.06
1
0.46
0.03
0.88
0.55
1
0.43
0.45
0.1
0.09
0.09
0.59
0.16
0.51
0.46
0.46
0.42
0.45
0.55
0.44
0.06
0.5
0.3
0.33
0.14
0.69
0.38
0.74
0.38
0.38
0.29
0.28
1863
1693
1684
1585
2290
2464
2549
2316
2600
2677
1479
1138
1576
2084
1726
1851
2310
2930
2576
1664
1237
2662
1575
1566
1326
1480
2161
1352
1648
2936
2404
1738
5228
2576
1586
1480
1917
1938
2110
1479
2576
2445
2185
2078
1674
1228
1375
64
64
64
64
64
64
64
64
64
64
64
64
64
82
64
71
64
64
64
64
64
64
64
64
64
64
64
64
64
64
64
64
64
64
64
64
64
64
64
64
64
82
64
64
64
64
64
0
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
0
0
0
0
0
1
0
1
1
0
0
1
1
1
0
0
1
0
0
0
0
1
1
0
0
1
1
1
0
0
1
3
3
3
3
4
5
4
4
4
4
3
2
3
4
3
2
5
4
4
3
2
5
3
2
2
3
4
2
3
3
4
3
4
4
3
3
4
3
4
3
5
4
3
4
3
4
2
1
1
1
1
1
1
1
1
1
1
0
0
0
1
1
2
1
1
1
1
0
1
1
0
1
0
1
1
0
1
1
0
4
1
1
0
1
1
1
0
1
2
1
1
1
0
1
220000
180000
203600
249900
193000
215000
201000
65000
195000
215900
92000
155000
123500
110400
198900
150000
104000
245000
180000
154300
170000
219000
295000
181500
260000
239900
135500
191500
225000
98500
110500
290000
184400
178500
415000
244900
150000
168000
159000
127000
175000
255250
175000
235000
324000
173000
116900
0.54
0.26
0.59
0.37
0.4
0.5
0.54
0.22
0.35
0.52
0.31
0.38
0.08
0.1
0.44
0.26
0.07
0.48
0.41
0.42
0.45
0.6
0.95
0.56
1.25
0.7
0.67
0.66
0.62
0.08
0.08
0.51
0.28
1
0.58
0.43
0.55
0.49
0.39
0.06
0.46
0.5
0.6
0.41
0.53
0.21
0.06
1650
1718
2576
2280
2088
1917
3140
1029
1896
2310
924
2080
1237
1287
1847
1064
1480
2462
2228
1260
1559
1980
2380
1887
2185
2488
1152
2025
2521
1480
1480
2362
1910
1952
3358
2090
1965
2110
1456
1479
1874
2099
1872
2388
2812
1064
1375
64
64
64
64
64
64
64
82
64
64
64
64
64
64
64
64
64
64
64
82
64
64
82
64
64
64
64
64
64
64
64
64
64
71
64
64
64
64
64
64
64
64
64
64
64
64
64
1
1
0
0
0
0
0
0
1
0
0
1
1
1
0
1
1
1
0
0
0
1
0
0
0
1
0
0
0
1
1
0
1
0
1
1
1
1
0
0
0
0
0
1
1
0
1
3
3
4
4
4
4
5
3
4
5
2
3
3
3
3
3
3
5
3
3
4
4
3
4
4
4
1
4
5
3
3
4
3
3
4
4
5
4
4
3
4
4
3
4
4
2
2
1
1
1
1
1
1
1
0
1
1
1
1
1
0
1
0
1
2
1
0
1
1
1
1
1
1
0
1
1
0
1
1
1
2
1
1
1
1
0
0
1
1
1
1
1
1
0
105900
112000
235000
235000
130000
235000
191900
284900
335000
140000
191000
153000
196000
248000
240000
132000
199000
217000
167000
245000
358000
412500
208000
270000
100000
130000
182500
139000
104000
221000
260000
182500
196000
132000
224900
199900
165835
189000
89900
235000
166000
153100
162000
224000
222400
199000
166000
0.09
0.13
0.72
1
0.18
0.74
0.48
0.58
0.01
1
0.41
0.51
0.55
0.46
0.6
0.19
1.42
0.69
0.51
0.29
0.06
0.6
0.53
0.38
0.74
0.56
0.71
2.84
0.09
0.52
1
0.5
0.43
0.09
0.11
0.24
0.39
0.8
0.19
0.59
0.48
0.46
0.4
0.52
0.86
0.46
0.95
1480
1260
2086
2588
1480
1752
2660
2417
2793
1152
2344
1926
2208
2208
2708
1142
2529
1797
1611
2576
2653
3896
1585
2774
1283
1136
1896
1536
1480
2096
2324
2079
1911
1480
2208
1462
1794
1886
1080
2576
1508
1672
1739
3074
1976
2302
1480
64
64
64
64
64
64
64
64
64
64
64
64
64
64
64
64
64
64
64
64
82
64
64
64
64
64
64
64
64
64
64
64
64
64
64
64
64
64
64
64
64
64
64
64
64
64
51
0
1
1
0
0
0
0
1
1
0
0
1
1
1
0
1
1
0
0
1
1
1
1
1
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
1
3
2
3
4
3
3
4
3
3
2
4
4
4
3
5
3
3
4
3
4
4
5
3
4
2
3
4
2
3
4
4
4
4
3
4
3
4
4
3
5
4
4
4
7
3
4
3
0
1
1
1
0
1
1
1
1
0
1
1
1
1
2
0
1
0
1
1
0
2
1
1
1
0
1
1
1
1
0
1
1
1
1
0
1
1
0
1
1
1
1
1
1
1
1
149900
152000
162500
274900
100000
215000
124000
125000
138000
225000
180000
189900
435000
120000
163000
131000
126500
122500
425000
225000
209000
189100
285000
266600
80000
225000
159000
119900
130900
194670
72000
144700
139500
319000
348000
189900
20000
60000
179500
133300
153000
111900
187000
158500
153000
190000
242000
0.63
0.42
0.34
0.5
0.2
2.96
1
1
1
0.52
0.48
0.33
1
2.6
0.15
2.8
0.08
0.14
0.46
0.63
3.8
0.46
0.98
1
1
6.07
0.03
0.18
0.11
0.28
0.18
0.16
0.15
0.5
3.68
0.98
0.52
0.01
0.91
0.34
2.06
0.35
0.47
0.7
0.39
0.52
1.27
960
1582
1600
2320
1034
1488
1056
864
1552
1816
1530
1756
4211
2206
1092
1594
1480
1480
3003
2164
1519
1604
1400
1752
880
1240
1514
840
840
2592
1010
1380
1366
1681
2037
2570
936
960
1352
1060
1508
1272
2389
1210
1230
1832
1854
54
36
54
54
54
57
57
57
57
57
57
54
57
57
36
36
54
54
57
57
57
57
57
57
57
57
36
36
36
36
36
36
36
57
36
36
20
41
30
41
30
60
27
60
60
60
60
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
4
4
2
3
3
3
3
3
3
4
5
3
2
7
3
3
4
2
2
3
3
4
2
3
3
1
2
4
3
3
3
3
3
3
2
2
3
4
3
4
6
2
3
4
3
0
0
0
0
0
0
0
0
1
1
1
0
2
1
0
0
1
1
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
1
1
1
1
234500
225000
165000
129900
315000
129900
257000
324000
520000
150414
290000
112000
185000
295000
290000
79900
256000
245000
140000
272000
164000
182500
219900
325000
352000
315000
154000
199000
202000
292000
116600
155000
215000
373490
259142
293565
285558
273960
185000
190000
171000
208000
168000
165000
138500
179900
180000
2
0.68
0.38
0.28
0.07
0.24
0.26
3.64
0.41
0.46
0.15
0.16
1
2.61
1
0.19
0.83
1
0.42
0.87
0.68
0.38
1.1
0.8
0.95
4.1
0.34
0.09
1
0.57
1
0.48
0.14
0.19
0.5
0.35
0.21
3.47
0.55
0.53
0.54
0.54
0.32
0.25
0.32
0.5
0.04
2268
1807
1272
1560
1863
1120
1832
2092
2702
1040
1758
2326
2340
2058
944
640
2353
2038
1469
2219
1774
1296
2289
2463
3126
2550
1182
1890
1944
2815
1040
1638
2206
3170
2328
2737
2879
2158
1336
1594
1603
2190
1478
1348
1558
1574
1612
60
60
60
47
47
47
47
47
47
47
47
27
27
27
27
20
60
54
60
63
54
60
60
60
54
54
60
60
36
57
57
57
57
57
57
57
54
54
57
54
57
57
54
54
54
54
54
0
0
0
1
1
0
1
1
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
1
1
0
1
1
1
1
1
0
1
3
3
4
3
3
2
2
4
3
3
2
3
3
3
1
2
4
4
4
3
4
4
4
5
4
3
2
4
3
4
3
4
4
4
4
4
4
3
3
3
3
4
3
2
3
3
4
0
1
1
1
1
0
1
1
1
1
1
0
0
1
1
0
1
1
0
1
0
1
1
2
0
0
0
1
1
1
1
0
1
1
1
1
0
1
1
0
0
0
1
0
1
1
0
112000
152000
100000
154000
133000
285000
138000
303000
250000
167500
190000
182500
107000
195000
169000
156000
120000
170000
249835
188095
176450
322277
149000
95000
198500
185000
168900
220000
129900
167000
330000
336000
512971
229000
145000
103000
210000
559000
218000
262138
125000
130000
157500
193000
275000
240000
200136
0.21
0.17
0.51
0.17
0.11
0.14
1
0.18
1.29
1
0.6
0.46
1.03
0.47
0.5
0.26
0.49
0.28
0.52
0.15
0.05
0.09
0.49
0.19
0.1
0.03
0.16
0.28
0.32
0.23
0.12
0.15
0.01
0.29
0.16
0.07
0.17
0.24
0.21
0.15
0.24
0.16
0.3
0.3
0.12
0.15
0.15
1216
2256
1170
1456
1320
2076
1326
2240
2100
1129
2296
1475
1268
1816
1632
1254
1272
1604
2474
2057
1852
2242
1564
960
1680
1428
1672
2284
1286
1250
1896
2592
1904
1680
1152
1290
2396
3090
1428
1631
1368
1134
1697
1666
1738
1457
1632
54
54
54
57
57
57
57
57
57
38
57
57
57
57
57
54
57
57
57
57
57
57
57
57
57
57
57
57
57
57
57
57
57
57
57
57
57
57
57
57
57
57
57
57
57
57
57
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
1
1
1
1
0
0
1
1
1
1
1
0
0
1
1
1
0
1
0
1
0
1
0
0
1
1
1
0
1
3
4
3
3
3
4
3
4
4
2
4
3
3
3
4
2
3
4
4
3
3
3
4
3
2
2
3
3
3
3
4
3
2
3
2
3
4
4
3
3
3
3
3
3
4
2
3
0
0
1
0
0
1
0
1
1
0
1
1
1
1
1
0
0
0
1
1
0
0
1
0
0
1
0
1
1
0
0
0
1
0
1
1
1
2
0
1
0
0
1
1
1
0
1
395000
366703
103150
310000
142900
359770
126000
760000
282500
132000
325000
207000
155000
330000
101760
496000
185000
125000
286000
269000
303374
371165
287600
131000
187000
169000
133500
620000
549254
280000
135000
195388
337020
330850
248495
120000
240000
235000
500075
240000
270000
225000
280000
225000
248220
275000
137000
1.4
0.15
0.25
0.17
0.36
0.16
0.68
1.22
0.25
0.06
0.23
0.48
0.24
0.12
0.15
0.34
0.11
0.25
0.13
0.04
0.12
0.39
0.07
0.34
1
0.04
0.21
1.06
0.25
0.09
0.26
0.14
0.15
0.46
0.63
0.26
0.48
0.22
0.91
0.07
0.46
0.12
0.16
0.48
0.46
0.03
0.12
2186
2117
936
3347
1824
2592
1080
3148
2128
1616
3313
2327
1640
1421
1280
3467
1250
1368
1396
2004
2242
2786
2242
1404
1600
1408
972
4856
2885
1560
1472
2124
2162
2515
2294
1744
2022
1578
3400
1744
2560
1398
2494
2208
2550
1812
1290
57
57
57
57
57
57
57
57
57
57
57
57
57
57
57
57
57
57
57
57
57
57
57
57
57
57
57
57
57
57
57
57
57
57
57
57
57
57
57
57
57
57
57
57
57
57
57
1
1
0
0
1
1
0
1
0
0
1
0
1
0
0
1
0
0
0
1
1
0
1
0
1
0
0
1
1
0
0
1
1
0
1
0
1
1
1
1
1
1
1
1
1
1
0
3
3
3
6
4
3
2
5
3
3
4
3
4
3
2
4
3
3
3
3
3
4
3
3
3
2
3
5
3
2
3
3
3
4
4
4
3
3
3
3
3
3
3
4
3
2
2
0
1
1
2
1
0
0
0
1
0
1
1
1
0
1
1
0
0
0
1
0
1
0
0
1
0
0
2
1
0
0
1
1
1
1
0
1
0
0
1
1
0
0
2
1
1
0
150000
649000
195000
373200
169450
144200
189900
166000
160000
327355
247000
318000
341000
288650
157000
449000
142000
389000
476000
249230
139900
301900
425000
121000
150000
138000
199900
145000
465000
158000
375000
147783
339000
267000
290000
271295
278140
138000
367500
428500
140000
140000
145000
280000
190400
267000
164900
0.14
1.04
0.49
0.65
0.15
0.15
0.5
0.14
0.23
0.14
0.29
0.23
0.23
0.08
0.03
1
0.16
1
0.42
0.18
0.3
0.73
1.03
0.25
0.19
0.29
0.39
0.27
0.25
0.32
0.27
0.36
0.36
0.07
0.12
0.35
0.62
0.07
0.27
0.42
0.48
0.36
0.3
0.07
0.17
0.11
0.14
1172
4128
1816
2628
1254
1660
1850
1258
1219
1850
2103
1806
1674
2242
1408
3457
1728
2354
2246
1902
1178
2896
2457
936
934
1279
1888
1686
2310
1200
1944
1184
2000
1744
1620
2359
2230
1147
2205
3243
1431
936
1368
1800
1920
1416
616
57
57
57
57
57
57
57
57
57
57
57
57
57
57
57
57
57
57
57
57
57
57
57
57
57
57
57
57
57
57
57
57
57
57
57
57
57
57
57
57
57
57
57
57
57
57
57
0
1
1
0
1
0
0
1
1
1
0
1
0
1
0
1
0
1
1
1
0
1
1
0
0
0
0
0
1
1
1
0
1
1
1
1
1
0
1
1
0
0
1
1
0
0
0
2
3
3
4
3
4
3
3
3
3
3
3
2
3
3
3
3
3
3
2
3
4
3
3
2
3
3
4
2
3
3
3
3
3
3
4
3
2
3
4
3
3
3
3
3
3
2
0
2
1
1
1
1
1
0
0
1
0
1
1
0
0
2
0
2
1
1
0
1
1
0
0
1
0
1
1
0
1
0
1
1
1
0
0
0
1
0
0
0
0
1
1
0
0
280000
225000
148000
165000
340455
133000
115540
240000
600000
71500
189900
325000
280000
255000
300000
106000
139000
165000
169000
159400
300000
161000
230500
220000
177900
350000
335000
597185
173000
518000
212000
149900
140958
95000
161600
351400
155000
198500
276000
167000
227000
405100
395000
360000
775000
285000
300000
0.1
0.11
0.06
0.32
0.38
0.42
0.2
0.58
0.04
0.3
0.03
0.08
0.14
0.12
0.2
0.48
0.27
0.06
0.17
0.24
0.87
0.23
0.59
0.41
0.29
0.32
0.14
1.07
0.33
0.17
0.5
0.87
0.22
0.33
0.24
0.15
0.3
0.4
0.21
0.25
0.84
0.39
0.14
0.41
0
0.07
0.12
1488
1320
1250
1286
2886
1279
1074
1304
3191
1056
1468
1598
1160
1028
2014
1296
932
1290
1448
1368
3046
1272
1822
1579
1660
2452
2004
4210
1640
2847
1816
2028
775
1368
936
1680
1368
1326
1579
1286
2132
2000
2222
2641
2472
1926
1534
57
57
57
57
57
57
57
57
57
57
57
57
57
57
57
57
57
57
57
57
57
57
57
57
57
57
57
57
57
57
57
57
57
57
57
57
57
57
57
57
57
57
57
57
57
57
57
0
0
1
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
1
0
1
0
0
0
0
1
0
1
1
0
1
1
1
0
1
1
1
4
3
2
3
4
3
3
3
3
3
3
3
3
2
6
3
2
3
2
3
4
3
4
4
4
3
3
4
4
3
3
4
2
2
3
2
3
3
3
3
3
3
3
4
3
2
3
0
1
0
1
1
1
0
1
2
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
1
0
1
1
0
0
0
0
1
0
1
1
0
2
1
0
0
1
2
0
214000
229000
330000
146000
381500
430000
650000
194500
279000
183000
195000
470000
167000
309278
217500
200000
199995
179000
329000
374900
165000
647000
315000
208000
405000
535000
184020
95000
87550
131000
127000
104695
120000
278500
75500
121900
208000
151000
138000
229000
130000
89900
145000
86000
95000
195000
107325
0.25
0.22
0.23
0.42
0.15
0.34
0.43
0.17
0.39
0.31
0.03
0.17
0.11
0.02
0.34
0.17
0.16
0.46
1
0.06
0.29
1.08
0.63
0.34
0.58
1
0.4
0.17
0.46
0.23
0.2
0.21
0.18
0.16
0.13
0.47
0.45
0.59
0.38
0.55
0.52
0.46
0.76
0.46
0.17
0.34
0.1
1490
1126
1435
1136
2162
2328
2754
1504
2473
2072
1480
2096
1050
1650
1596
979
1393
864
2744
2300
1612
2640
775
2470
3124
3254
1544
1410
906
1512
1232
921
1287
2600
1302
1144
1703
1553
1040
2124
1344
884
1812
880
1256
1826
1134
57
57
57
57
57
57
57
57
57
57
57
57
57
57
57
57
57
57
57
57
57
57
57
57
57
57
57
38
38
38
38
38
38
38
38
38
38
38
38
38
38
38
38
38
38
38
38
0
0
1
0
1
1
1
0
1
0
1
0
0
1
1
0
1
0
1
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
3
3
3
3
3
3
4
4
4
3
3
2
2
3
3
2
2
4
3
3
4
1
4
4
4
3
6
2
3
3
2
3
4
3
3
3
3
2
4
3
2
3
3
3
3
3
0
1
0
0
1
1
1
0
1
1
1
2
0
1
0
0
0
0
0
1
1
1
0
1
1
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
131000
166900
127000
119000
92509
174000
180000
155000
146500
162500
210000
165000
123000
150000
128900
88100
175000
120975
147543
118000
199000
79900
279000
90000
91900
153000
170000
145200
296000
150000
86000
118000
155000
222500
250000
365000
120000
193000
85568
82000
225000
240000
234900
112000
261000
400000
310000
0.54
0.75
0.43
0.15
0.52
0.46
0.52
0.41
0.44
0.46
0.48
0.65
0.08
0.58
0.14
0.14
0.68
0.13
0.29
0.22
0.5
0.18
0.55
0.28
0.35
0.25
2.68
0.2
0.02
0.37
0.45
0.36
0.75
0.69
0.46
0.69
0.89
0.47
0.15
0.46
0.77
0.85
0.01
0.02
0.57
0.6
0.41
1916
1272
960
1152
840
2106
1632
1092
1634
1890
2224
1475
1480
1368
1200
840
1176
1380
1786
1480
1574
950
3178
1342
1336
1542
2272
1480
2506
1852
1055
1392
1608
1564
2068
2516
1684
1481
999
896
792
2747
2277
1281
2462
2897
2672
38
38
38
38
38
38
38
38
57
57
57
57
54
54
36
36
47
36
36
54
54
54
57
57
57
54
54
54
57
30
57
57
57
57
57
57
38
57
20
20
20
27
63
63
63
63
63
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
1
1
1
4
3
3
2
2
5
3
3
3
3
5
3
3
3
3
2
3
3
3
3
3
2
4
3
2
3
4
2
4
4
2
3
3
3
4
4
4
3
3
2
2
4
4
2
4
4
4
1
0
0
0
0
0
0
0
1
1
2
1
1
1
0
0
0
0
0
0
1
0
1
0
1
0
1
1
2
0
1
0
1
1
1
0
0
0
0
0
1
2
0
1
1
2
1
182000
187500
405000
420000
359000
120000
171500
159900
186500
260000
115000
191000
355465
339900
90000
245000
320900
159000
174900
293500
210000
182500
219900
370000
286000
169900
161000
287000
315000
177000
332000
249000
179000
150000
225000
182000
329900
165000
180000
321000
180000
178000
279900
179000
183000
500000
170000
0.29
0.47
0.61
1.14
0.48
0.01
0.31
0.21
0.21
0.46
0.01
0.44
0.35
0.57
0.49
0.04
0.46
0.22
0.62
0.49
0.51
1
0.46
0.46
0.47
0.49
0.23
0.36
0.94
0.34
1
0.53
0.09
0.52
0.37
0.33
0.5
0.33
0.31
0.53
0.11
0.14
0.55
0.14
0.15
1
0.37
1932
1320
3296
3279
3204
1217
1782
1180
1452
2140
1219
1518
3328
2344
960
1544
2873
1180
1368
1904
1320
1594
1847
3125
2004
1623
1120
2363
2572
1548
2734
1462
1558
1664
1877
1838
2368
2104
1180
2399
1232
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999
63
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349900
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10300
95000
0.34
0.32
0.33
0.15
0.32
0.16
0.16
0.06
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0.15
0.15
0.15
0.31
0.16
0.15
0.46
0.16
0.33
0.33
0.49
0.32
0.94
0.16
0.36
0.16
0.35
0.15
0.16
0.16
0.35
0.16
0.15
0.43
0.15
1
0.33
0.16
0.59
0.4
0.35
0.44
0.14
0.37
1
1.96
0.16
0.15
2102
1656
1561
988
1765
912
1592
1344
1385
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912
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1974
988
1508
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1748
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1900
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1080
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1040
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1988
672
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912
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54
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265000
185000
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125000
349900
142000
132500
220000
160000
156900
138000
166000
195000
0.15
0.31
0.15
0.15
0.16
0.06
0.16
0.15
0.15
0.15
0.31
0.16
0.15
0.46
0.16
0.33
0.33
0.49
0.32
0.94
0.16
0.36
0.16
0.35
0.15
0.16
0.16
0.35
0.16
0.15
0.43
0.15
1
0.33
0.16
0.59
0.4
0.35
0.44
0.14
0.37
1
1.96
0.28
0.31
0.25
0.56
1385
1508
1385
1628
1592
1344
1385
1385
1679
908
1527
912
1184
1719
1080
2118
2527
1592
1294
1974
988
1508
908
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912
912
988
1748
912
1385
1300
908
1900
2191
1080
1300
2458
1040
2886
1840
1988
672
1512
1635
1672
1892
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54
54
54
54
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63
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63
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63
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63
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205100
330000
179000
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66000
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454900
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165000
329000
49387
0.6
0.47
0.05
0.58
0.29
1
0.5
0.57
0.08
0.2
0.3
0.65
0.56
0.7
0.6
2.85
0.47
0.06
0.41
0.57
0.48
0.53
12.2
0.61
0.49
0.6
0.12
0.15
0.77
0.26
0.66
0.57
0.47
0.48
0.46
0.57
0.43
0.58
0.15
0.14
0.4
0.1
0.5
0.42
0.09
0.46
0.48
2513
3336
1302
2006
1836
1994
1652
1888
1480
1234
1778
2514
2700
2330
2676
2180
2284
1314
2396
2088
2310
2040
2599
1702
2125
2310
1431
924
1799
976
2217
1969
2376
1585
1453
2973
1612
2734
1479
945
1938
1364
3242
1571
1314
2413
900
63
63
63
63
63
60
63
63
63
63
63
63
63
63
63
60
63
63
63
63
63
63
63
63
63
63
63
63
60
63
63
77
63
63
63
63
63
63
63
63
63
63
63
63
63
63
77
1
1
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445000
73000
125000
146500
209000
196500
157000
125500
190000
250000
255000
129700
65000
107000
255000
398000
176000
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220000
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177555
95000
5000
264900
315000
155000
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238000
224000
211000
279000
242000
199875
259900
200000
212000
230000
189000
313635
185000
239900
202000
155000
120000
78000
0.58
0.28
0.13
0.12
0.45
0.46
0.29
0.06
0.44
0.49
0.4
0.15
0.34
0.28
0.57
0.61
0.45
0.86
0.38
0.5
0.35
0.13
0.56
0.2
0.29
0.5
0.77
0.09
0.22
0.71
0.33
1
0.23
0.11
0.61
0.46
1.28
0.71
0.47
0.42
1.93
0.48
0.42
0.48
0.12
1.48
0.33
3157
908
924
1138
2310
1874
1228
1479
1612
2088
2131
924
1692
1568
2262
2960
1683
2680
2742
2012
2702
1314
1672
1200
1700
2652
3062
1290
1012
2310
2026
1404
1782
2002
1782
2212
1872
1804
1910
1632
3824
1196
2259
1690
1227
1278
668
63
60
63
63
63
63
63
63
63
63
63
63
60
63
77
63
63
63
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63
63
63
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63
63
63
63
63
63
60
63
63
63
63
63
63
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63
63
63
63
63
63
60
1
0
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1
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311000
198000
158500
227000
265900
163000
165000
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200000
299900
210000
220000
326900
204900
234000
236000
124000
199100
245000
264000
105000
187000
127000
100000
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105000
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149900
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124500
424200
120000
205000
175000
295000
156500
143000
215000
287000
122500
180000
143000
137000
271000
0.46
0.32
0.92
0.46
0.34
0.23
0.28
0.07
0.29
0.77
0.33
0.66
1
0.39
0.31
0.42
0.46
0.14
0.5
0.35
0.15
0.32
0.17
0.48
0.77
0.95
0.53
0.06
0.46
0.18
0.47
0.47
0.19
1.82
0.21
0.42
0.36
0.49
0.21
0.09
0.29
0.4
0.23
1
0.09
0.08
0.47
2762
1558
1352
1920
1940
1249
1576
1419
1700
2748
1792
1724
2692
1734
2014
2056
1745
1352
2259
2572
924
2000
929
1540
1730
1500
2522
1479
1922
1215
2772
2574
945
2914
1480
1914
1354
2302
1234
1480
1665
2182
924
1220
1480
1375
2003
63
63
63
63
63
63
63
63
63
63
63
63
63
63
63
63
63
63
63
60
63
63
63
77
63
63
63
63
63
63
63
63
63
63
63
63
63
63
63
63
63
63
63
63
63
63
63
1
0
0
0
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1
1
1
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1
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0
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1
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1
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0
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1
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4
3
3
5
3
3
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4
3
3
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3
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4
2
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3
2
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2
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129900
133000
179000
302000
168000
120000
119000
168000
124900
415000
150000
310000
157000
205000
275000
320000
380000
119900
345000
145000
123000
202500
182000
175000
132500
239000
86125
245000
229900
129000
200000
144200
166000
178000
165000
218000
175000
145000
195000
288139
187500
255000
145000
183000
318310
192500
195000
0.07
0.06
0.25
0.72
0.92
0.19
0.07
0.35
0.98
2.92
0.99
4
0.46
0.8
0.46
0.46
0.74
0.46
0.82
0.46
0.07
0.79
1
0.63
0.21
0.41
0.01
1.28
1.64
0.33
0.09
1.19
0.4
0.9
1
0.1
0.02
0.18
0.76
0.46
0.59
0.91
1
0.46
0.23
1.2
1
1480
1480
1456
1888
1112
1480
1480
1836
1522
2709
1020
2208
1368
2488
1865
3174
2944
960
3142
1666
708
1598
1564
1224
1379
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960
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1820
1632
1594
1290
1560
1453
1664
2169
1420
1441
1016
2947
1652
1927
960
1804
2616
1116
2147
54
54
54
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54
54
54
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36
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27
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64
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21
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36
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62
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62
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62
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62
62
62
62
1
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138000
230000
237500
375000
105000
168000
221000
135000
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344100
112000
380000
125000
145000
190000
135000
58500
80500
150410
170000
242551
176500
212000
135000
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262000
155000
207000
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111000
97000
200000
230000
299900
183855
174900
335000
208000
380000
289900
188000
600000
262000
220000
275000
215000
0.87
0.79
1
4.84
0.16
1
0.29
0.31
0.39
1.05
1
0.3
0.6
5.52
0.48
0.15
0.04
0.01
0.25
1
2
0.29
1
0.41
0.89
0.46
1
0.27
0.14
0.42
0.74
0.1
1.73
0.47
0.62
0.34
0.34
3.28
0.47
2
0.3
0.41
0.99
0.29
2.03
0.61
0.46
876
2102
1776
1996
1759
1014
2270
1548
1620
2608
1080
1140
1152
1056
1257
936
1140
960
1058
768
2048
1198
2430
918
2722
2364
1440
1744
2280
1736
883
1001
1296
2304
2076
1468
1272
1900
1548
2212
2376
1712
2660
1487
1532
2486
1918
62
62
62
62
35
62
35
27
35
52
35
50
36
36
62
35
33
33
35
35
52
33
50
50
50
33
50
50
33
33
50
50
50
40
52
52
52
43
52
52
52
52
62
36
36
62
62
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
1
0
2
4
3
3
3
3
4
3
3
4
3
3
3
2
3
2
3
2
2
2
4
2
4
3
4
4
3
3
4
3
1
2
3
3
3
4
3
3
3
4
4
3
4
3
3
4
3
2
1
1
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
1
1
0
1
1
0
1
1
1
1
0
1
1
0
100000
158500
148900
218000
355840
168000
171000
195000
201880
145000
206000
78000
320900
159000
180000
129900
150000
171134
151000
100000
655000
243500
265000
400000
272800
255000
220000
775000
233000
216977
245000
159000
725000
268300
159000
155000
345000
165200
185000
225500
420000
220000
620000
260000
359900
375000
302900
0.51
0.17
0.15
0.45
0.87
0.08
0.58
0.41
0.46
0.47
0.01
0.14
0.47
0.61
0.16
0.05
0.38
0.25
0.37
0.31
0.19
0.29
0.18
0.24
0.08
0.17
0.13
0.48
0.14
0.48
0.03
0.24
0.21
0.16
0.28
0.3
0.29
0.3
0.53
0.28
0.11
0.18
0.53
0.35
0.5
0.14
0.22
1270
1406
1385
1300
3259
1536
1636
1944
1676
1040
1800
1394
1885
1056
1593
1436
1668
1302
1239
840
780
1728
1666
2022
2225
1023
1290
3968
1699
2137
1428
936
2586
1373
1272
1368
2120
1279
1104
1092
2247
1146
3250
1920
1932
1620
1640
21
40
40
40
40
36
35
35
35
36
36
21
21
21
62
62
62
62
62
62
62
62
62
62
62
62
62
62
62
62
62
62
62
62
62
62
62
62
62
62
62
62
62
62
62
62
62
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
1
0
0
1
1
1
0
0
1
1
0
1
0
0
0
0
1
0
1
0
3
2
2
3
4
3
4
3
3
3
3
3
2
3
3
4
4
3
3
2
2
3
3
3
4
2
2
5
4
4
2
3
4
3
3
3
4
2
2
3
4
4
3
4
3
3
3
0
0
0
0
1
0
1
1
1
0
1
1
1
0
0
0
1
0
1
0
0
0
0
1
1
0
0
4
0
0
1
0
1
1
0
1
1
0
0
1
0
0
2
1
1
0
0
175000
260000
270000
485000
200000
367000
175000
203000
170000
375000
159900
230000
375000
421000
218000
167850
252500
650000
380000
214500
218500
174000
225000
309750
658300
203000
375000
62500
205000
84500
280500
182000
571000
168000
354000
238000
182000
218500
227500
375000
399900
360000
412500
268500
300300
382500
189000
0.17
5.35
0.33
0.24
0.57
0.03
0.3
0.04
0.16
0.31
0.25
0.14
0.12
0.31
0.28
0.27
0.21
0.34
0.04
0.21
0.17
0.16
0.46
0.07
0.69
0.06
0.03
1
0.19
0.2
1.09
0.02
1
0.25
0.46
0.2
0.16
0.17
0.55
0.5
0.09
0.34
0.39
0.18
0.13
0.19
0.3
1040
1676
1991
1908
966
1815
1664
1216
1564
2752
936
1617
1452
1911
1580
1920
1155
3770
1675
912
1510
864
1600
1744
3208
1290
1900
2808
1576
1118
1752
1753
2186
1800
2462
1286
1337
1170
1185
2424
1828
2176
2000
1340
1208
2244
1592
62
62
62
62
62
62
62
62
62
62
62
62
62
62
62
62
62
62
62
62
62
62
62
62
62
62
62
35
35
35
35
35
62
62
62
62
62
62
62
62
62
62
62
62
62
62
62
0
1
1
1
0
1
0
1
1
1
0
0
0
1
1
1
0
1
1
0
0
1
1
1
1
1
1
0
0
0
1
0
1
0
1
0
1
0
0
1
0
1
1
1
0
1
0
5
4
3
4
3
2
3
2
3
4
3
4
3
3
3
3
4
4
2
3
3
2
4
3
4
2
2
3
3
3
3
3
3
2
5
5
3
2
3
4
3
4
3
3
3
4
3
0
0
1
1
0
1
0
1
0
1
0
0
1
1
0
1
0
1
1
0
0
0
0
1
1
0
1
0
0
0
2
0
0
0
1
0
0
1
0
1
0
1
1
1
0
1
1
295000
220000
223000
399000
169480
347750
455000
249900
250000
265000
670000
195000
360000
175000
166500
190100
180500
440000
170000
220000
70500
65000
127500
155000
255500
136000
204000
200000
163000
149350
235000
260000
210000
159900
209000
135000
200000
432600
195000
165000
198000
219000
430000
120000
373735
183853
213500
0.39
0.01
0.12
0.25
0.24
0.15
0.25
0.04
0.05
0.32
0.11
0.11
0.13
0.4
0.1
0.48
0.75
0.19
0.51
0.63
0.09
0.13
0.19
0.57
0.92
0.35
0.86
0.8
0.36
0.44
0.25
0.65
0.46
0.7
0.55
0.35
0.96
0.54
0.47
0.52
0.15
0.65
1.34
0.17
0.53
0.14
0.46
1831
1093
1460
2128
1368
2200
2310
1776
1852
1092
2247
1311
1392
1116
812
1872
1248
1702
1346
1596
884
814
720
2051
1590
1202
2016
1274
960
1056
1820
2486
1890
1274
1716
1336
1392
2346
1475
1248
1920
2040
2649
1500
3163
1343
1573
62
62
62
62
62
62
62
62
62
62
62
62
62
62
62
52
40
52
52
52
36
36
36
36
36
36
36
36
36
36
36
62
62
36
36
62
62
62
62
27
27
27
21
64
64
64
64
1
0
0
0
0
1
1
1
1
1
0
1
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
1
1
0
1
0
0
1
0
0
0
1
1
1
3
2
2
3
3
3
2
3
3
2
4
3
3
4
2
4
3
2
2
3
3
2
2
3
2
3
3
3
3
3
3
4
3
4
4
2
3
4
3
3
4
4
3
3
4
2
3
1
1
0
1
0
1
1
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
1
0
1
0
1
1
1
155000
197000
392499
229900
289250
189900
397200
389405
135000
174000
525000
135000
412000
186000
453935
355000
186000
197000
180000
178000
305000
262000
225000
403040
388500
417000
410000
170000
295000
216000
221649
199900
463000
146500
225000
160000
275055
315513
323759
167500
272699
177500
128000
317105
144500
260000
244000
0.09
0.41
0.48
0.44
0.42
0.12
0.46
0.35
0.66
0.13
0.46
0.01
0.62
0.08
0.58
0.69
0.35
0.14
0.13
0.47
0.33
0.46
0.89
0.49
0.46
0.13
0.5
0.35
0.01
0.38
0.37
0.21
0.64
0.02
0.24
0.16
0.46
0.46
0.35
0.92
0.3
0.31
1
0.44
0.15
0.33
0.33
1270
1316
3092
1328
2560
1343
3250
3086
1080
1120
2876
1281
2900
1512
2879
2537
1056
1296
1512
1338
2368
1528
1857
3320
2227
2742
2988
1656
1760
1702
1682
1180
2885
1281
1596
1184
2745
2680
2483
1188
2366
1508
792
3285
1673
2000
1561
64
64
64
64
64
64
64
64
64
64
64
64
64
64
64
64
64
64
64
64
64
64
64
64
64
64
64
64
64
64
64
64
64
64
64
40
40
40
40
40
40
40
40
40
40
64
40
1
0
1
0
0
1
1
1
0
1
1
1
1
1
1
1
0
0
1
0
1
1
1
1
1
1
0
1
0
0
0
1
1
1
1
0
1
1
0
0
1
0
0
0
0
0
0
3
3
4
3
4
2
4
3
2
2
5
2
4
2
4
4
3
2
2
3
4
3
4
4
4
4
5
3
3
4
3
2
4
2
3
3
4
4
3
3
4
3
2
4
2
4
3
1
0
1
1
1
1
1
1
1
1
1
0
1
1
1
1
0
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
0
1
0
1
1
1
0
1
1
0
1
0
0
1
287989
159000
167000
348000
140000
145000
150450
230000
147423
223000
167500
299000
235900
147000
305000
154000
149000
300279
278000
202000
328463
185000
128000
335000
148900
229900
215000
253000
304065
222000
165000
275000
325000
406000
230000
125000
148000
279000
250000
314940
165900
150000
133000
155000
220000
229000
177000
0.4
0.16
0.16
0.17
0.17
0.15
0.17
0.95
0.16
0.33
0.16
0.1
0.59
0.24
0.53
0.17
0.15
0.54
0.64
0.47
0.49
0.45
0.17
0.92
0.16
0.43
0.49
0.45
0.34
0.34
0.15
0.37
0.27
1.08
0.31
0.04
0.41
0.44
0.62
0.37
0.16
0.75
0.15
0.37
0.41
1.61
0.63
2828
1592
1184
1708
1276
1184
908
1612
912
1508
1492
874
1573
1227
2494
912
988
2762
2625
1222
3144
1173
908
2274
908
1540
1196
1780
2670
1581
1592
2011
1391
2636
1656
1518
1182
1836
1529
2715
1184
1120
1008
1008
2077
1572
1874
40
40
40
40
40
40
40
64
40
40
40
40
64
64
64
40
40
40
64
64
40
40
40
64
40
40
64
40
40
40
40
40
40
40
40
64
64
64
64
40
40
36
36
36
36
36
36
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
4
3
3
2
2
2
2
3
2
3
3
3
4
3
3
2
2
4
4
2
4
3
2
4
2
3
4
3
4
3
3
4
2
4
3
3
3
3
2
4
2
3
3
3
3
3
4
1
0
0
1
1
0
0
1
1
1
0
1
1
1
1
0
0
1
1
0
1
1
0
1
0
0
1
1
1
1
0
1
1
3
1
0
1
0
1
1
0
0
0
0
1
0
0
120000
195000
315371
137000
225700
204900
189500
374000
319000
294100
440760
128000
239505
141700
215500
320210
273495
256350
255000
124000
293000
147000
284595
342269
229000
216900
164900
149000
150000
214990
173000
149900
155000
170000
237500
297065
342202
345264
325046
367000
159900
145000
272500
163255
319000
160600
246000
0.11
0.29
1
0.36
0.36
0.34
0.34
0.72
0.35
0.39
0.38
0.16
0.37
0.15
0.34
0.81
0.3
0.35
0.33
0.09
1.94
0.15
0.32
0.39
0.51
0.31
0.15
0.15
0.18
0.32
0.14
0.17
0.15
0.16
0.37
0.45
0.44
0.88
0.5
1
0.17
0.16
0.32
0.09
0.47
0.15
0.34
768
1552
2331
960
1720
1437
1510
3021
1960
2112
2917
912
2244
1202
2601
2492
2680
2271
2012
920
2111
1184
2627
2641
1736
1656
1168
1385
969
1508
1602
912
1128
1514
1535
2722
2711
3020
2712
2556
1184
912
2212
1602
3285
1406
1472
36
36
36
36
64
64
64
28
64
64
64
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
40
64
40
40
40
40
40
40
40
40
40
40
64
40
40
40
40
40
40
40
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
1
1
0
0
1
2
3
4
2
3
3
3
4
4
3
4
2
3
2
4
3
4
3
3
3
3
3
4
4
3
3
3
2
2
3
2
2
2
3
3
4
4
4
4
4
3
2
4
2
4
2
3
0
1
1
0
0
0
0
1
0
1
1
1
1
0
1
1
0
1
1
0
1
1
1
1
1
1
1
1
0
1
1
1
0
1
0
0
1
1
0
1
0
1
1
1
1
0
1
153000
295000
159000
148400
311000
314000
250000
149000
307890
223000
219000
178000
295925
141160
229900
254900
126000
176500
161800
112200
154500
300000
206000
257000
182000
161000
176000
177160
355063
213000
266500
285000
178900
300000
211000
451000
201400
195900
190000
150000
206000
285000
120000
377500
340000
240000
295000
0.17
0.48
0.16
0.15
0.54
0.53
0.4
0.16
0.55
0.33
0.47
0.48
0.56
0.17
0.34
0.33
0.85
0.37
0.34
0.14
0.54
0.92
0.1
0.75
0.38
0.59
0.42
0.41
0.36
0.48
0.52
0.36
0.35
0.56
0.49
2
0.49
0.4
0.57
0.21
1
0.32
0.2
1
0.55
0.45
0.49
1072
2504
1184
912
2120
3344
2243
908
2714
1360
1719
1404
2134
912
1423
2044
896
1380
960
840
1820
2144
1610
1752
1729
1056
1292
832
2256
1274
1608
1868
1554
3604
1887
1326
1876
1672
2064
1138
1814
2380
976
2886
2483
1846
2592
40
64
40
40
40
40
40
40
40
40
64
64
40
40
40
40
36
36
36
36
36
36
36
36
36
36
64
64
64
64
64
64
64
64
64
64
64
64
64
64
64
64
64
64
64
64
64
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
1
1
0
1
0
0
1
2
5
2
2
3
4
3
2
4
3
3
3
4
2
3
3
2
3
3
2
4
3
3
3
4
3
3
3
4
3
3
3
3
6
4
3
3
3
4
2
3
4
2
4
4
3
4
0
1
0
1
0
1
1
0
0
1
1
1
1
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
1
1
0
1
0
1
1
0
1
1
1
1
1
1
0
2
1
1
1
215000
275000
189000
156000
410000
264500
145500
116500
264500
215000
263000
243000
203000
335000
385000
210000
154000
155000
165000
300000
240000
182000
194000
410000
280000
235000
185000
167000
206500
165000
230000
235000
200500
310000
169900
210500
305000
508000
220000
256000
196900
233000
140000
162900
178000
265000
454900
0.63
0.47
0.81
0.09
0.79
0.46
0.09
0.08
0.44
0.3
0.6
0.57
0.29
0.61
0.5
0.59
0.14
0.17
0.17
0.7
0.46
0.35
6.15
0.44
0.85
0.47
0.06
0.21
0.5
0.05
0.35
0.73
0.69
0.46
0.06
0.28
0.92
0.17
0.41
0.5
0.41
0.26
0.06
0.12
0.17
0.67
0.66
1792
2588
1210
1290
2444
2376
1480
1375
2676
1778
2570
1272
1852
2298
2259
2426
1480
1244
1479
2358
1453
2080
1960
2600
1897
1872
1260
1228
1956
1480
1793
2078
1666
2378
1452
1792
2290
3511
1922
2263
1672
1902
1479
1314
1302
2310
2880
64
64
64
64
75
64
64
64
64
64
64
64
64
64
64
64
64
64
64
64
64
64
64
64
64
64
64
64
64
64
64
64
64
64
64
64
75
64
64
64
64
64
64
64
64
64
64
1
0
0
1
0
0
0
1
0
0
0
0
1
1
1
0
0
1
0
0
1
1
0
1
1
0
1
1
1
1
1
0
1
0
1
0
0
0
0
0
1
1
1
0
1
0
0
3
4
3
2
4
4
3
2
4
3
5
2
3
4
4
4
3
2
3
4
4
4
3
4
4
4
2
3
4
3
4
4
3
3
3
3
4
4
4
4
4
3
2
2
2
5
4
0
1
0
1
1
2
0
0
1
1
1
0
1
1
1
1
1
0
0
0
1
1
1
1
1
1
1
1
0
0
1
1
1
1
1
1
1
1
0
1
0
1
1
1
0
1
1
215000
248000
395000
171500
268000
166500
355000
165000
300000
350000
279900
265000
267000
235000
299900
167000
168000
150000
255000
455000
351100
315000
220000
159000
341000
276000
309000
217021
188500
320000
247000
166000
236000
233900
162740
225000
360000
281520
365000
315000
297900
270000
260000
72000
229500
275000
155000
5.65
0.67
0.7
0.07
0.48
0.06
0.43
0.93
0.08
0.5
0.49
0.65
0.31
0.76
0.46
0.07
0.4
0.07
0.41
4.2
0.46
0.46
0.4
0.14
0.57
0.47
0.49
0.46
0.05
0.55
0.34
0.1
0.15
0.3
0.07
0.45
0.91
0.56
0.56
0.6
0.3
0.42
0.42
0.33
0.34
0.54
0.29
1948
1613
2803
1479
2147
1314
2330
1352
2276
2162
2091
2564
2050
1768
2497
1290
1776
1480
1910
2828
2535
2576
1500
1480
2250
1831
2214
1846
1302
2212
1783
1480
1794
1918
1480
1756
2499
2310
2950
2702
2288
1838
2310
1152
1577
2175
1375
64
64
64
64
64
64
64
64
64
64
64
64
64
64
64
64
64
64
64
64
64
64
64
64
64
64
64
64
64
64
64
64
64
64
64
64
64
64
64
64
64
64
64
52
64
64
64
1
1
1
1
1
1
1
0
0
1
1
0
0
0
1
1
0
0
1
1
0
0
0
0
1
1
1
0
1
1
0
0
0
1
0
0
1
1
0
1
1
1
0
0
0
0
0
2
3
4
3
4
2
4
3
5
4
4
4
4
3
3
2
3
3
4
3
4
4
3
3
3
3
4
3
2
4
4
2
3
4
3
4
4
5
4
4
3
4
4
3
3
4
2
1
1
1
1
1
1
1
0
1
1
1
1
0
0
1
1
0
0
0
1
1
1
0
0
1
1
1
0
0
1
1
1
0
1
1
1
1
1
1
3
1
0
1
0
0
1
0
225570
224000
290000
262000
319900
265000
255000
217300
291000
319000
271500
224900
260000
199900
252659
312500
290000
155000
355000
190000
130000
264000
193980
219900
469900
314230
138900
160000
228000
224400
132870
135600
150600
335000
316250
181280
158000
221000
230000
299000
148000
267500
259000
321000
409790
184000
145000
0.37
0.54
0.61
0.64
0.34
0.45
0.33
0.35
0.49
0.46
0.54
0.48
0.63
0.63
0.41
0.46
0.46
0.57
0.55
0.83
0.06
0.21
0.31
0.25
1.4
0.51
0.15
0.29
0.25
5
0.06
0.51
0.07
1.25
0.04
0.39
0.73
0.23
0.5
0.1
0.07
0.24
0.01
0.1
0.27
0.45
0.07
1616
1954
2728
2553
1963
2564
1792
1663
2070
2588
2276
1732
2310
1742
2802
1902
2030
1498
2116
2108
1480
2427
1348
1391
3422
2686
1034
1072
1512
1008
1480
912
1480
1558
2648
2248
1461
1470
1900
2054
1480
1822
1620
2120
3009
1791
1480
64
64
64
64
64
64
64
64
64
64
64
64
64
52
64
64
64
75
64
64
40
40
40
40
62
62
40
40
40
40
40
40
40
62
62
40
40
40
40
62
40
40
62
62
62
40
40
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
1
1
0
1
0
1
0
0
0
1
1
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
3
4
4
4
4
4
3
3
4
4
5
4
5
4
4
4
4
2
3
4
2
3
2
3
4
4
2
2
3
2
3
3
3
3
4
4
3
3
3
4
2
3
3
4
5
4
2
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
0
0
0
1
1
0
0
0
0
1
0
1
1
1
0
0
1
0
0
1
0
1
0
1
0
1
310000
170000
210500
199900
150000
153000
334000
216900
259000
240000
186030
203000
255000
119000
260800
169000
225000
124000
245000
250000
172000
153500
165000
159000
171500
240000
409550
302000
285000
385900
140595
213000
335000
290000
265000
334000
382406
149300
212000
195000
245000
422680
240000
156000
265000
334000
382406
1.75
0.07
0.02
0.24
0.28
0.11
0.55
0.4
0.05
0.3
0.37
0.43
0.13
0.09
0.5
0.19
0.95
0.35
0.51
0.48
0.46
0.48
0.02
0.17
0.17
0.51
0.69
0.61
0.38
0.4
0.42
0.47
0.47
0.66
0.49
0.32
0.44
0.16
0.34
0.46
0.36
0.16
4.21
0.16
0.49
0.32
0.44
1300
1480
1876
1564
1248
1480
2281
2395
1915
1400
1104
1796
1512
1646
1868
1301
1652
1056
2312
2072
1200
1764
960
988
1514
1320
2719
1796
1709
3008
1350
1200
1857
2305
2184
1668
2712
912
1508
1232
1836
4486
2204
1184
2184
1668
2712
40
40
40
40
40
40
62
40
40
40
40
40
40
40
40
40
62
62
62
62
62
62
62
51
51
61
61
61
61
61
61
61
61
51
51
51
51
51
51
61
51
51
51
51
51
51
51
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
1
1
1
1
0
1
0
0
0
0
0
0
0
1
0
1
3
3
3
3
3
2
4
3
4
3
4
3
3
3
3
3
3
3
3
3
2
3
3
2
3
3
3
3
3
4
3
3
3
4
3
3
4
2
3
3
4
6
3
3
3
3
4
0
1
0
0
0
0
1
1
1
2
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
1
1
0
0
1
1
1
0
1
0
0
1
1
1
2
0
1
0
1
149300
212000
195000
171600
245000
282000
260000
254500
179900
255000
265000
174000
322000
337000
221450
247000
180000
229900
230000
388000
350000
169700
190000
317500
70000
300000
145400
183500
275900
436023
319900
249000
289000
285000
194900
125000
111300
0.16
0.34
0.46
0.32
0.36
0.87
0.34
0.17
0.07
0.53
0.43
0.06
0.26
0.46
0.36
0.3
0.54
0.37
0.54
0.77
0.66
0.07
0.53
0.54
1.34
0.65
0.13
0.28
0.81
0.41
0.58
0.43
0.38
0.94
0.39
0.24
0.59
912
1508
1232
960
1836
1836
1803
1463
1290
2310
1664
1479
2483
2480
2699
1676
2816
1966
2112
2762
2184
1480
1624
1650
1313
2600
945
1121
2288
2718
2464
2426
2310
2564
1099
1225
1959
51
51
61
61
51
61
61
61
61
61
61
61
61
61
61
61
61
61
61
61
61
61
61
61
61
61
61
61
61
61
61
61
61
61
51
51
51
0
0
0
0
0
1
0
1
1
0
1
0
1
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
3
3
3
4
4
4
3
2
5
3
3
4
4
6
3
5
3
4
4
3
3
3
3
2
4
2
3
3
4
4
4
5
4
2
3
3
0
0
1
0
1
1
0
1
1
1
1
0
1
1
1
1
1
0
1
1
1
0
0
1
0
1
0
0
1
1
1
2
1
1
0
1
0
Bathrooms
1
2.5
1
1.5
1
1
1.5
1.5
1.5
1.5
1
2
1
2
1.5
1
1.5
2.5
1
1
1
1.5
2.5
2
1.5
3
1
1.5
2
1.5
1
2.5
2
2.5
2.5
3
2.5
2.5
3
2.5
1.5
2.5
1.5
2.5
2.5
2.5
1
2.5
2
2
2.5
2.5
2
2
1.5
1
2.5
1.5
2.5
2
2
1.5
1
1.5
1
2.5
1
2.5
2
2
2.5
1.5
4
2.5
2
2.5
1.5
2
2.5
1
2.5
2.5
1.5
2.5
2.5
2
2
1.5
1
1.5
1.5
1.5
1
1.5
2.5
1.5
2
1
2
1
1
1
1.5
1.5
2.5
2
2.5
2.5
1
1
1
1.5
2
1
2.5
2.5
1.5
2.5
2
2
1
1
2.5
1
2
2.5
2
1
2
1
1
1
1
2.5
1.5
1
1.5
1
1
1.5
2.5
1.5
2.5
1
2.5
2
1
1.5
2
1.5
2.5
1.5
2.5
1.5
2.5
2.5
1.5
1
2.5
2.5
1
2.5
2.5
2.5
2.5
2.5
2.5
1.5
1.5
2.5
2.5
2
2.5
1.5
3.5
2.5
2.5
2.5
3.5
1
1
2
1.5
2
1.5
2
2.5
1.5
2
2.5
1.5
2.5
1
1.5
1.5
1.5
1
1
2
1.5
2.5
2
1.5
1.5
1.5
2.5
1
1.5
2.5
2.5
2.5
1.5
1.5
1.5
2
2
1.5
2
1.5
2
2.5
1.5
1
2.5
2.5
1.5
1.5
1.5
1.5
1.5
2
2
1
2
2
1.5
1.5
2
2
1.5
1.5
2
1.5
1
1.5
1
1.5
2.5
2.5
1.5
2.5
1
2.5
1.5
1.5
1
1.5
1.5
2.5
1.5
2
2
2.5
2
1.5
2
1.5
1.5
1
2.5
1
1.5
1.5
2.5
3
1
1.5
2.5
1.5
1.5
2.5
2.5
1.5
2.5
1.5
3
2.5
2.5
2.5
2.5
2.5
1.5
1
2.5
2.5
2
2
2.5
2.5
2.5
2
1.5
2.5
1.5
1.5
1.5
1.5
2.5
1.5
1.5
3.5
2.5
1.5
4
2.5
1.5
1.5
2.5
1.5
2.5
1.5
2.5
2.5
2.5
2.5
1.5
1.5
1.5
2
1.5
2.5
2.5
2.5
2.5
3.5
1
2.5
2.5
1
2.5
1.5
1.5
2.5
1
1.5
3.5
2.5
1
2.5
2.5
2.5
2.5
1.5
2.5
2
2.5
2.5
1.5
1.5
2.5
1.5
2
3.5
2.5
2
1.5
2.5
1.5
2.5
2.5
2.5
2.5
2.5
2
1.5
1.5
1.5
2.5
2.5
1.5
2.5
2.5
2.5
2.5
1
2.5
1.5
2.5
2.5
2.5
1.5
2
2
1.5
2.5
2.5
4.5
1
2.5
1
1
2.5
1
1.5
2.5
2.5
2.5
1.5
1.5
2.5
2.5
1.5
2.5
1.5
3
1.5
1
1.5
2.5
2.5
2.5
2
2
1.5
1
2.5
1.5
1.5
1
1
2
1.5
2
2
3.5
2.5
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1
Office 2016 – myitlab:grader – Instructions
Excel Project
Descriptive Numerical Analysis V3
Project Description:
The present study investigates the distribution of sale prices for homes in a region in upstate New York. This
project will also seek to compare the distributions of sale prices between homes with central air and homes
without central air. Suppose you are being transferred to this area and are interested in getting a good
description of selling prices for homes in this region. The variables collected in the data are: Price: Recorded in
dollars; Lot size: measured in acres; Living Area: measured in square feet; Pct College: percent of students going
to college; Central Air: No – 0, Yes – 1; Bedrooms: Number of bedrooms; Fireplace: Number of fireplaces;
Bathrooms: Number of bathrooms. For the purpose of this project, you will only be using the variables Price and
Central Air.
Instructions:
For the purpose of grading the project you are required to perform the following tasks:
Step
1
Points
Possible
Instructions
Start Excel. Download and open the workbook named:
Descriptive_Numerical_Analysis_Start.
0
Obtain the descriptive statistics for sale prices for all homes in the dataset.
2
Adding Descriptive Statistics
Go to the Data worksheet. Select Data Analysis in the Analysis group of the Data tab of the
Ribbon (note you should add this Add-in in case you do not have it in the Data tab already).
Select Descriptive Statistics and click OK. Select the Price column as the Input Range. Choose
Grouped by Columns. Check the ‘Labels in the first row’ box. Choose cell I1 on the Data
worksheet as the output range. Check the ‘Summary statistics’ box. Do not check any
additional boxes in the Descriptive Statistics menu.
8
In cell I16 on the Data worksheet, type Q1. In cell J16, calculate the value of the first
quartile for the Price data set.
In cell I17 on the Data worksheet, type Q3. In cell J17, calculate the value of the third
quartile for the Price data set.
In cells D7-D14 on the Problem worksheet, identify the values for the mean, standard
deviation, minimum, first quartile, median, third quartile, maximum, and sample size. Round
the monetary values to the nearest cent.
3
In cell D18, identify the range of sales prices.
1
4
In cell D19, calculate the size of the bins for 25 bins.
1
5
To construct the histogram, first create a column of ‘bins’ on the Data worksheet. Since the
bin size is not a round number in thousands of dollars, choose the bin size to be 30,000. In
cell K1 on the Data worksheet, type Binsize. In cell K2, type 30000, in cell K3, type
60000, and then drag the sequence down until you pass the most expensive selling price.
4
Now construct the histogram.
Inserting the Histogram
Updated: 05/20/2018
1
Current_Instruction.docx
Office 2016 – myitlab:grader – Instructions
Step
Excel Project
Points
Possible
Instructions
On the Data worksheet, select Data Analysis in the Analysis group of the Data tab of the
Ribbon. Select Histogram and click OK. Select the Price column as the Input Range and the
Binsize column (starting on cell K1) as the Bin Range. Check the ‘Labels’ box. Choose cell M1
on the Data worksheet as the output range. Check the ‘Chart Output’ box. Do not check any
additional boxes in the Descriptive Statistics menu.
Moving the Histogram
Select the Histogram. Then choose Move Chart in the Design tab on the Ribbon. Select the
Problem worksheet in the provided drop-down menu. Drag the histogram on the Problem
worksheet and change its size so that it is located in cell C23.
Edit Chart Elements
Change the title of the histogram to Distribution of selling prices. Right click on one of the
bars and select ‘Format Data Series’. Slide the ‘Gap Width’ to zero.
6
In cells F26-G26, choose how you would describe the shape of the distribution from the
drop-down menu.
1
7
In cells F27-G27, choose which measure of 'center' is best to describe the distribution from
the drop-down menu.
1
8
In cells F28-G28, choose how to compare the values of the mean and the median from the
drop-down menu.
1
9
In cells F29-G29, choose which measure of 'spread' is best to describe the distribution from
the drop-down menu.
1
In cell D34, calculate the percentage of homes rounded to one decimal place whose prices
are expected to exceed $300,000 using the value(s) found in step 5.
10
11
12
Note: Using the Histogram tool, a value is included in a particular bin if the number is greater
than the lowest bound and equal to or less than the greatest bound for the data bin.
In cell D36, calculate the percentage of homes rounded to one decimal place that are priced
between $90,000 and $300,001, exclusive, using the value(s) found in step 5.
Note: Using the Histogram tool, a value is included in a particular bin if the number is greater
than the lowest bound and equal to or less than the greatest bound for the data bin.
In cell D38, calculate the percentage of homes rounded to one decimal place expected to be
priced less than or equal to $150,000 using the value(s) found in step 5.
1
1
1
Note: Using the Histogram tool, a value is included in a particular bin if the number is greater
than the lowest bound and equal to or less than the greatest bound for the data bin.
Construct two histograms showing the distribution of prices for homes without central air and
the prices for homes with central air.
13
First, create the two columns of data. On the Data worksheet, copy the Price column to
columns P and Q. In cell P1, type Price without central air. In cell Q1, type Price with
central air. Then select the first row, go to the Home tab of the Ribbon, and select
Sort&Filter in the Editing group. Select Filter in the drop-down menu. In cell E1, open the
drop-down menu and select to show only value 0. Delete all of the filtered values in column
Q. Then in cell E1 in the drop-down menu, select to show only value 1. Delete all of the
filtered values in column P. Go back to cell E1 and select to show all values.
Updated: 05/20/2018
2
8
Current_Instruction.docx
Office 2016 – myitlab:grader – Instructions
Step
Excel Project
Points
Possible
Instructions
Construct the histogram using Data Analysis for the Price without central air column using the
Binsize column K (starting on cell K1). Choose cell R1 on the Data worksheet as the output
range. Be sure to check the ‘Labels’ and ‘Chart Output’ boxes in the Histogram menu. Move
the histogram to the Problem worksheet and place it in cells B42-C42. Change the title of
the histogram to Distribution of selling prices without central air. Right click on one of
the bars and select ‘Format Data Series’. Slide the ‘Gap Width’ to zero.
Construct the histogram using Data Analysis for the Price with central air column using the
Binsize column K (starting on cell K1). Choose cell T1 on the Data worksheet as the output
range. Be sure to check the ‘Labels’ and ‘Chart Output’ boxes in the Histogram menu. Move
the histogram to the Problem worksheet and place it in cells D42-G42. Change the title of
the histogram to Distribution of selling prices with central air. Right click on one of the
bars and select ‘Format Data Series’. Slide the ‘Gap Width’ to zero.
Obtain the descriptive statistics for sale prices for homes without central air. Go to the Data
worksheet and use Descriptive Statistics in Data Analysis for the Price without central air
column. Choose cell V1 on the Data worksheet as the output range. Be sure to check the
‘Labels in the first row’ and ‘Summary statistics’ boxes.
14
In cell V16 on the Data worksheet,
quartile for the Price without central
In cell V17 on the Data worksheet,
quartile for the Price without central
type Q1. In cell W16, calculate the value of the first
air data set.
type Q3. In cell W17, calculate the value of the third
air data set.
7
In cells D45-D51 on the Problem worksheet, identify the values for the minimum, first
quartile, median, mean, third quartile, maximum, and sample size. Round the monetary values
to the nearest cent.
Obtain the descriptive statistics for sale prices for homes with central air. Go to the Data
worksheet and use Descriptive Statistics in Data Analysis for the Price with central air column.
Choose cell X1 on the Data worksheet as the output range. Be sure to check the ‘Labels in
the first row’ and ‘Summary statistics’ boxes.
15
In cell X16 on the Data worksheet,
quartile for the Price with central air
In cell X17 on the Data worksheet,
quartile for the Price with central air
type Q1. In cell Y16, calculate the value of the first
data set.
type Q3. In cell Y17, calculate the value of the third
data set.
7
In cells E45-E51 on the Problem worksheet, identify the values for the minimum, first
quartile, median, mean, third quartile, maximum, and sample size. Round the monetary values
to the nearest cent.
In cells D55 and D56, compare the estimated sale prices of homes with central air to homes
without central air. Choose the correct answers from the drop-down menus.
16
In cell E58, calculate the expected difference in median costs. In cells D60, F60, D61, and
F61, identify the variability of prices using Q1 and Q3 for each data set. Use the descriptive
statistics in cells D45-E51. Keep the same number of decimal places as the values in step14
and step15.
7
17
Save the workbook. Close the workbook and then exit Excel. Submit the workbook as directed.
0
Total Points
Updated: 05/20/2018
3
50
Current_Instruction.docx
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