2 homework assignments for statistics

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Urqen97

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2 assignments for statistics both around 10 questions each, shouldn't take more than 40 minutes each page maximum

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MATH 185 - Elementary Stats I Name___________________________________ ©W p2d0O1S8t KKnuMtoa^ wS]oXfStxwhaKrfe^ OLEL]Cy.] K nAIlsla GrhiSg]hztHsB `rEe]sgeWrSvveNdL. HW #2 Date________________ Find the median, mean, and sample standard deviation for each data set. (Each worth 6 points) 1) Test Scores 38 43 44 44 50 50 50 53 48 2) Educational Attainment by US State 48 3) State % Bachelor's Degree Tennessee 23 Vermont 33.1 Delaware 28.7 Virginia 34 Michigan 24.6 Louisiana 21.4 Massachusetts 38.2 Oregon 29.2 Pennsylvania 26.4 Average Time to Maturity Plant Days Radish 22 Kale 60 Swiss Chard 60 Soy Bean 70 4) 49 Plant Days Carrots 70 Bell Pepper 75 Sugar Baby Watermelon 75 Honeydew 80 Plant Days Red Potato 80 Beefsteak Tomato 80 Seedless Watermelon 85 Radicchio 90 Plant Celery Tomatillo Parsnip Horseradish Days 95 100 105 150 Annual Precipitation (Inches) 34.8 51.6 31 44.6 48.8 56.8 57.6 68.2 11.6 34.4 5.6 17 31.4 15.8 69.4 5) Birth Rate Country Births/woman Country Births/woman Country Births/woman Lithuania Germany 1.29 1.43 Uruguay Sweden 1.84 1.88 Laos Vanuatu 2.9 3.36 Bulgaria Cuba 1.44 1.46 Qatar Mongolia 1.92 2.22 Togo Rwanda 4.53 4.62 San Marino Brazil 1.49 1.69 United Arab Emirates Malaysia 2.36 2.58 São Tomé and Príncipe Liberia 4.67 4.81 Lebanon St. Kitts & Nevis 1.74 1.78 Algeria Honduras 2.78 2.86 Mali 6.16 Worksheet by Kuta Software LLC -1- ©e E2x0c1V8O WK\uutXaI DSDoHfHtIwmaTrkeh cLZLJCf.s d qAXlzlN arciggDh\tmsS ^roeAsXejrsvUeodC.S r dM[aSdZep Nw]imtRhO \I\nDfUi_n^iltCec CAMl`gpeCbrrVaF k1s. 6) Minutes to Run 5km 28 26.9 22.4 31.8 34.6 43.5 25.9 41.8 28.3 28.1 42.2 22 30.7 41.6 29.7 26.5 36.6 19.9 27.4 32 43.7 40.6 37.7 Comparing Coefficient of Variation. (Worth 2 points) 7) If the Coefficient of Variation for an English test is 6.9%, and the CVar for a history test is 4.9%, compare the variations. (In other words which has more variation) Find the coefficient of variation. (Each worth 2 points) 8) The average IQ of the students in on statistics class is 110, with a standard deviation of 5; the average IQ of students in another class is 106, with a standard deviation of 4. Which class is more variable in terms of IQ? 9) The average age of the accountants at Three Rivers Corp. is 26, with a standard deviation of 6; the average salary of the accountants is $31,000, with a standard deviation of $4000. Compare the variations of age and income. Find the coefficient of of variation for each of the two sets of data, then compare the variation. (Worth 6 points) 10) CUSTOMER WAITING TIMES Waiting times (in minutes) of customers at the Jefferson Valley Bank (where all customers enter a single waiting line) and the Bank of the Providence (where customers wait in individual lines at three different teller windows) are listed below. Jefferson Valley (single line): 6.5 6.6 6.7 6.8 7.1 7.3 7.4 7.7 7.7 7.7 Providence (individual lines): 4.2 5.4 5.8 6.2 6.7 7.7 7.7 8.5 9.3 10.0 Worksheet by Kuta Software LLC -2- ©Y Z2x0V1^8E dKPuPtcan mSroef[thw^a\rLeY LLyLWCy.K t MAflFln IrGiRgPhRtQsw ArreKsYesrLvceVdB.P ` xMZaldneu FwEi^tfhi jIPnNfZiinCi[tDez JAUlIg_ebbLraam r1F. 1) (9 points) Below are the heights of children and their parents. Gender M M M M M M M M M M M M M M M M M F F F F F F F F F F F F F F F F F F Mother's Height 66 58 68 64 62 66 63 65 64 64 62 62 67 63 66 65 71 63 64 60 65 67 59 60 58 72 63 67 62 63 64 63 64 60 65 Father's Height 70 69 71 68 66 74 73 69 67 68 72 72 68 71 67 71 75 64 67 72 72 72 67 71 66 75 69 70 69 66 76 69 68 66 68 Offspring's Height 62,5 64,6 73,9 67,1 64,4 71,1 71 69,3 64,9 68,1 66,5 66,5 70,3 67,5 68,5 71,9 67,8 58,6 65,3 61 65,4 67,4 60,9 63,1 60 71,1 62,2 67,2 63,4 62,2 64,7 59,6 61 64 65,4 a) Calculate the mean and median of the mother's height. b) Calculate the mean and median of the father's height. c) Calculate the mean and median of the offspring's height. 2) (9 points) Below are the heights of children and their parents. Gender M M M F F Mother's Height 66 64 69 67 69 Father's Height 64 62 66 65 62 Offspring's Height 69,1 67,4 67,5 64,7 68,4 a) Calculate the mean and median of the mother's height. b) Calculate the mean and median of the father's height. c) Calculate the mean and median of the offspring's height. 3) (4 points) Based on your calculations what kind of observations did you make? 4) (10 points) Median Household Income By State State Alabama Alaska Arizona Arkansas California Colorado Connecticut Delaware District of Columbia Florida Georgia Hawaii Idaho Illinois Indiana Iowa Kansas Kentucky Louisiana Maine Maryland Massachusetts Michigan Minnesota Mississippi Missouri Montana Nebraska Nevada New Hampshire New Jersey New Mexico New York North Carolina North Dakota Ohio Oklahoma Oregon Pennsylvania Puerto Rico Rhode Island South Carolina South Dakota Tennessee Income 43.623 72.515 50.255 41.371 61.818 60.629 70.331 60.509 70.848 47.507 49.620 69.515 47.583 57.574 49.255 53.183 52.205 43.740 45.047 49.331 74.551 68.563 49.576 61.492 39.665 48.173 47.169 52.997 51.847 66.779 72.093 44.963 59.269 46.868 57.181 49.429 46.879 51.243 53.599 19.350 56.852 45.483 50.957 45.219 a) Construct a grouped frequency distribution using eight classes. b) Construct a histogram. Does the data resemble a normal distribution? Texas Utah Vermont Virginia Washington West Virginia Wisconsin Wyoming 53.207 60.727 55.176 65.015 61.062 41.751 53.357 58.840 5) (15 points) Below are the high temperatures of January 2017. 56 25 49 52 47 46 29 46 50 39 46 41 53 49 56 57 57 60 61 37 72 53 61 35 65 49 45 27 43 50 49 48 42 50 63 57 48 41 41 a) Find the median of the data set b) Find the first and third quartiles of the data set. c) Find the Interquartile Range (IQR) d) Find the upper and lower outlier boundaries e) List all the values, if any, that are classified as outliers. 6) (15 points) Below are the high temperatures of January 2018. 26 26 35 27 21 21 23 39 51 43 62 64 62 28 32 43 37 47 51 63 61 65 68 a) Find the median of the data set b) Find the first and third quartiles of the data set. c) Find the Interquartile Range (IQR) d) Find the upper and lower outlier boundaries e) List all the values, if any, that are classified as outliers. 7) (4 points) Draw a boxplot of each data set. Describe the distribution of each set. 8) (15 points) Below are the high temperatures of February 2017. 51 50 40 41 54 61 73 74 53 39 53 55 47 46 55 42 51 68 71 68 58 63 75 82 71 52 59 67 a) Find the median of the data set b) Find the first and third quartiles of the data set. c) Find the Interquartile Range (IQR) d) Find the upper and lower outlier boundaries e) List all the values, if any, that are classified as outliers. 9) (15 points) Below are the high temperatures of February 2018. 54 43 36 37 39 43 43 38 46 50 68 65 43 53 74 67 44 51 50 78 82 67 51 61 71 a) Find the median of the data set b) Find the first and third quartiles of the data set. c) Find the Interquartile Range (IQR) d) Find the upper and lower outlier boundaries e) List all the values, if any, that are classified as outliers. 59 62 62 10) (4 points) Draw a boxplot of each data set. Describe the distribution of each set.
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MATH 185 - Elementary Stats I

HW#2
Find the median, mean, and sample standard deviation for each data set. (Each worth
6 points)
1)

Test Scores
38
50

43
50

44
50

44
53

48

48

49

Median:
38 43 44 44 48 48 49 50 50 50 53

Median:
38 + 43 + 44 + 44 + 48 + 48 + 49 + 50 + 50 + 50 + 53
11
𝑋̅ = 47
Standard Deviation:
𝑋̅ =

𝑠=√

(38 − 47)2 + (43 − 47)2 + (44 − 47)2 + ⋯ + (50 − 47)2 + (53 − 47)2
11 − 1
𝑠 = 4.2895

2) Educational Attainment by US State
State
Tennessee

% Bachelor's Degree
23

Vermont

33.1

Delaware

28.7

Virginia

34

Michigan

24.6

Louisiana

21.4

Massachusetts

38.2

Oregon

29.2

Pennsylvania

26.4

Median:
21.4 23 24.6 26.4 28.7 29.2 33.1 34 38.2

Median:
21.4 + 23 + 24.6 + 26.4 + 28.7 + 29.2 + 33.1 + 34 + 38.2
9
𝑋̅ = 28.733
Standard Deviation:
𝑋̅ =

𝑠=√

(21.4 − 28.73)2 + (23 − 28.73)2 … + (34 − 28.73)2 + (38.2 − 28.73)2
9−1
𝑠 = 5.543

3)

Average Time to Maturity
Plant
Radish

Days
22

Plant
Carrots

Days
70

Plant
Red Potato

Days
80

Plant
Celery

Days
95

Kale

60

Bell Pepper

75

Beefsteak Tomato

80

Tomatillo

100

Swiss Chard

60

Sugar Baby Watermelon

75

Seedless Watermelon

85

Parsnip

105

Soy Bean

70

Honeydew

80

Radicchio

90

Horseradish

150

Median:
22 60 60 70 70 75 75 80 80 80 85 90 95 100 105 150
The median is: 80
Median:
𝑋̅ =

22 + 60 + 60 + 70 + 70 + 75 + 75 + 80 + 80 + 80 + 85 + 90 + 95 + 100 + 105 + 150
16

𝑋̅ = 81.06

Standard Deviation:
(22 − 81.06)2 + (60 − 81.06)2 … + (105 − 81.06)2 + (150 − 81.06)2
𝑠=√
16 − 1
𝑠 = 26.67

4)

Annual Precipitation (Inches)
34.8

51.6

31

44.6

48.8

56.8

57.6

68.2

11.6

34.4

5.6

17

31.4

15.8

69.4

Median:
5.6 11.6 15.8 17 31 31.4 34.4 34.8 44.6 48.8 51.6 56.8 57.6 68.2 69.4
The median is: 34.8
Median:
𝑋̅
=

5.6 + 11.6 + 15.8 + 17 + 31 + 31.4 + 34.4 + 34.8 + 44.6 + 48.8 + 51.6 + 56.8 + 57.6 + 68.2 + 69.4
15

𝑋̅ = 38.573

Standard Deviation:

𝑠=√

(5.6 − 38.57)2 + (11.6 − 38.57)2 … + (68.2 − 38.57)2 + (69.4 − 38.57)2
16 − 1
𝑠 = 20.305

5)

Birth Rate
Country
Lithuania

Births/woman
1.29

Germany

1.43

Bulgaria

1.44

Cuba

Country
Uruguay

Births/woman
1.84

Country
Laos

Births/woman
2.9

Sweden

1.88

Vanuatu

3.36

Qatar

1.92

Togo

4.53

1.46

Mongolia

2.22

Rwanda

4.62

San Marino

1.49

United Arab Emirates

2.36

São Tomé and Príncipe

4.67

Brazil

1.69

Malaysia

2.58

Liberia

4.81...


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