# Calculating the Measure of Central Tendency

Based upon the following chart please respond to the problems listed below the chart.

Standard Test Scores

Name Gender Absences PE Math Writing Reading

Alex Boy 5 49 85 86 80

Anthony Boy 18 51 39 71 75

Douglas Boy 1 82 74 78 79

Jorge Boy 4 56 66 68 60

Joshua Boy 5 83 79 78 77

Luke Boy 0 94 89 84 84

Robert Boy 17 36 36 56 50

Rupert Boy 4 24 55 56 52

Seth Boy 0 61 92 89 83

Wayne Boy 1 65 92 96 91

Blair Girl 3 94 59 66 90

Brooke Girl 2 75 35 43 46

Carmen Girl 0 49 91 91 90

CharlitaGirl 16 23 49 55 49

Kim Girl 2 71 90 92 95

Li Girl 1 73 98 93 95

Rachel Girl 2 92 87 92 91

Sara Girl 3 33 87 93 94

Sheetal Girl 0 18 100 97 97

Tawayna Girl 14 31 65 55 63

a. Calculate all measures of central tendency for data that are interval or ratio in measurement.

b. Calculate the standard deviation for data that are interval or ratio in measurement.

c. Assume this is a sample of students, calculate a t-test that compares boys and girls on the number of absences(there is an assumption of equal variances. Is there a significant difference in absences between gender?

d. Assume this is a sample of students and that students receive an A grade if their score is 90 or above. Calculate a chi-square test to determine whether girls achieve more A grades than boys in math. Calculate a chi-square test to determine whether girls achieve more A grades than boys in reading.

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Descriptive statistics

Absences PE Math Writing Reading

count 20 20 20 20 20

mean 4.90 58.00 73.40 76.95 77.05

sample variance 36.83 617.05 457.52 286.26 302.79

sample standard deviation 6.07 24.84 21.39 16.92 17.40

minimum 0 18 35 43 46

maximum 18 94 100 97 97

range 18 76 65 54 51

sum 98.00 1,160.00 1,468.00 1,539.00 1,541.00

sum of squares 1,180.00 79,004.00 116,444.00 123,865.00 124,487.00

deviation sum of squares (SSX) 699.80 11,724.00 8,692.80 5,438.95 5,752.95

standard error of the mean 1.36 5.55 4.78 3.78 3.89

1st quartile 1.00 35.25 58.00 63.50 62.25

median 2.50 58.50 82.00 81.00 81.50

3rd quartile 5.00 76.75 90.25 92.00 91.00

interquartile range 4.00 41.50 32.25 28.50 28.75

mode 0.00 49.00 92.00 78.00 91.00

b. Calculate the standard deviation for data that are interval or ratio in measurement.

Using Microsoft excel

Add- Ins Megastat descriptive statistics

Absences PE Math Writing Reading

sample standard deviation 6.07 24.84 21.39 16.92 17.40

c. Assume this is a sample of students, calculate a t-test that compares boys and girls on the number of absences(there is an assumption of equal variances. Is there a significant difference in absences between gender?

Boys Absences Girl Absences

5 3

18 2

1 0

4 16

5 2

0 1

17 2

4 3

0 0

1 14

Solution:

Null Hypothesis:

H0: µ1 = µ2

H0: There is no significant difference in absences between gender.

Alternative Hypothesis:

H1: µ1 ≠ µ2

H1: There is a ...