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Assessment
WSS Techno Company manufactures computer terminals. The following data are
numbers of computer terminals produced at a company for a sample of 15 days. 20, 20,
15, 7, 22, 17, 22, 18, 19, 12, 15, 16, 22, 13, and 17. Calculate the range, average
deviation, variance, standard deviation, midhinge, interquartile range, and quartile
deviation. Say something about the data. What does it tells you?
RANGE
Range: Highest Value Lowest Value
Range= 22 7
Range= 15
The range of the number of computer terminals produced at WWS Techno
Company for a sample of 15 days is 15.
AVERAGE DEVIATION UNGROUPED DATA

󰇛
󰇜



 
The Average Deviation of the number
of computer terminals produced at WWS techno
company for a sample of 15days is 6.2.
VARIANCE
//
20
3
3
20
3
3
15
-2
2
7
-10
10
22
5
5
17
0
0
22
5
5
18
1
1
19
2
2
12
-5
5
15
-2
2
16
-1
1
22
5
5
13
-4
4
17
0
0
∑X=225
=0
=
93
x
x -
(x -
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Mean Formula:



VARIANCE
󰇛

󰇜






STANDARD DEVIATION
=
7
-10
100
12
-5
25
13
-4
16
15
-2
4
15
-2
4
16
-1
1
17
0
0
17
0
0
18
1
1
19
2
4
20
3
9
20
3
9
22
5
25
22
5
25
22
5
25

󰇛
󰇜
󰇛
󰇜

The Variance of the number of computer terminals
produced at WWS techno company for a sample of 15 days
is 17.71.
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=


=


= 17
Standard Deviation Formula:
󰇛

󰇜






󰇛
󰇜

The Standard Deviation of the number of computer terminals produced at WWS
techno company for a sample of 15 days is 4.21.
MIDHINGE
Midhinge

Midhinge

20
3
20
3
15
-2
7
-10
22
5
17
0
22
5
18
1
19
2
12
-5
15
-2
16
-1
22
5
13
-4
17
0
∑X=225
=0
The Midhinge of the number of computer
terminals produced at WWS techno company for a sample
of 15days is 17.5.
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Midhinge

Midhinge 
INTERQUARTILE RANGE
IQR =
IQR = 20 15
IQR = 5
QUARTILE DEVIATION
QD =

QD =

QD =
QD = 2.1
Range is commonly used to describe data spread. It only makes use of two data
observations. The average deviation is used to help summarize a collection of data. The
Variance of a set of numbers measures how far apart they are from their average value.
The standard deviation is a number that indicates how far apart measurements for a
group are from the average (mean or expected value).
The first and third quartiles are represented by the midhinge. The Interquartile Range is
a measurement of how far apart data points in a set are from the mean of the data set.
The quartile deviation is useful for examining the spread of a distribution around a
measure of its central tendency, typically the mean or average. All of the data gathered
above was calculated in these, using various formulas. Although we do not get the
entire data set at first in Range because it only uses two observations, as we progress
through the formulas from Variance to Quartile Deviation, we tend to have a larger data
set and calculation. It all shows that WSS Techno Company, which manufactures
computer terminals, has calculated the data set produced at a company for a 15-day
sample.
The Interquartile Range of the number of
computer terminals produced at WWS techno company
for a sample of 15days is 5.
The Quartile Deviation of the number of computer
terminals produced at WWS techno company for a sample of
15days is 2.1.

Unformatted Attachment Preview

Assessment WSS Techno Company manufactures computer terminals. The following data are numbers of computer terminals produced at a company for a sample of 15 days. 20, 20, 15, 7, 22, 17, 22, 18, 19, 12, 15, 16, 22, 13, and 17. Calculate the range, average deviation, variance, standard deviation, midhinge, interquartile range, and quartile deviation. Say something about the data. What does it tells you? RANGE Range: Highest Value – Lowest Value Range= 22 – 7 Range= 15 The range of the number of computer terminals produced at WWS Techno Company for a sample of 15 days is 15. AVERAGE DEVIATION UNGROUPED DATA 𝑥 𝑥−𝑥 20 20 15 7 22 17 22 18 19 12 15 16 22 13 17 ∑X=225 3 3 -2 -10 5 0 5 1 2 -5 -2 -1 5 -4 0 ∑𝑥 − 𝑥=0 /𝑥 − 𝑥 / 3 3 2 10 5 0 5 1 2 5 2 1 5 4 0 ∑𝑥 − 𝑥= 93 𝐴𝐷 = 𝐴𝐷 = ∑(𝑥 − 𝑥) 𝑛 93 15 𝐴𝐷 = 6.2 The Average Deviation of the number of computer terminals produced at WWS techno company for a sample of 15days is 6.2. VARIANCE x x-𝑥 (x - 𝑥 )² Mean Formula: 7 12 13 15 15 16 17 17 18 19 20 20 22 22 22 -10 -5 -4 -2 -2 -1 0 0 1 2 3 3 5 5 5 100 25 16 4 4 1 0 0 1 4 9 9 25 25 25 ∑ 𝑥 = 255 ∑(𝑥 − |𝑥) = 0 ∑(𝑥 − |𝑥)² = 248 𝑥= ∑𝑥 𝑛 255 𝑥= 15 𝑥 = 17 VARIANCE 𝑠2 = ∑(𝑥−𝑥)2 𝑛−1 𝑠2 = 248 15 − 1 𝑠2 = 248 14 𝑠 2 = 17.71 STANDARD DEVIATION 𝑥= ∑𝑥 𝑛 The Variance of the number of computer terminals produced at WWS techno company for a sample of 15 days is 17.71. 𝑥= 7+12+13+15+15+16+17+17+18+19+20+20+22+22+22 15 𝑥= 255 15 𝑥 = 17 Standard Deviation Formula: ∑(𝑥−𝑥)2 𝑛−1 𝑠=√ 𝑥 − 𝑥⁄ 2 𝑥 𝑥−𝑥 20 20 15 7 22 17 22 18 19 12 15 16 22 13 17 ∑X=225 3 3 -2 -10 5 0 5 1 2 -5 -2 -1 5 -4 0 9 9 4 100 25 0 25 1 4 25 4 1 25 16 0 ∑𝑥 − 𝑥=0 ∑𝑥 − 𝑥=248 248 𝑠 = √15−1 24𝛿 𝑠 = √ 14 𝑠 = 4.21 ∑(𝑥 − 𝑥)² = 248 The Standard Deviation of the number of computer terminals produced at WWS techno company for a sample of 15 days is 4.21. MIDHINGE Midhinge 𝑄1 +𝑄3 2 Midhinge 5+20 2 The Midhinge of the number of computer terminals produced at WWS techno company for a sample of 15days is 17.5. Midhinge 35 2 Midhinge 17.5 INTERQUARTILE RANGE IQR = 𝑄3 − 𝑄1 IQR = 20 – 15 The Interquartile Range of the number of computer terminals produced at WWS techno company for a sample of 15days is 5. IQR = 5 QUARTILE DEVIATION QD = 𝑄3 −𝑄1 2 QD = 20−15 2 5 QD = 2 The Quartile Deviation of the number of computer terminals produced at WWS techno company for a sample of 15days is 2.1. QD = 2.1 Range is commonly used to describe data spread. It only makes use of two data observations. The average deviation is used to help summarize a collection of data. The Variance of a set of numbers measures how far apart they are from their average value. The standard deviation is a number that indicates how far apart measurements for a group are from the average (mean or expected value). The first and third quartiles are represented by the midhinge. The Interquartile Range is a measurement of how far apart data points in a set are from the mean of the data set. The quartile deviation is useful for examining the spread of a distribution around a measure of its central tendency, typically the mean or average. All of the data gathered above was calculated in these, using various formulas. Although we do not get the entire data set at first in Range because it only uses two observations, as we progress through the formulas from Variance to Quartile Deviation, we tend to have a larger data set and calculation. It all shows that WSS Techno Company, which manufactures computer terminals, has calculated the data set produced at a company for a 15-day sample. Name: Description: ...
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