Question

****Please answer them all, if you cannot, please skip****

Here are scores received by a class of Biology students on a 40 point exam. Each number is the score, out of 40 points, received by one student. The data are separated by gender.

Scores, out of 40 points, received by female students:
17, 20, 30, 31, 31, 33.6, 34, 34.5, 35, 35, 36, 35.6, 36, 36, 36, 37, 37.5, 37, 38, 38

Scores, out of 40 points, received by male students:
11.5, 21.5, 22.5, 22.5, 23.5, 26, 28, 29, 30.5, 30.5, 30.5, 31, 32, 32.8, 34, 34, 35.4, 36, 36.5

1) On average, grades for females in this class go up from the female Mean exam score to _______ points.

Choose from the following options:

37, 37.18, 37.2, 39, 109.6

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2) On average, grades for females in class go down from the female Mean exam score to ______ points.

Choose from the following options:

29.6, 29.1, 29.0, 27.8, 20.6

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3) What is the Average Deviation in the exam scores for male students?

Choose from the following options:

92.7 points, 6.3 points, 6 points, 4.9 points. 4.8 points

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4) On average, grades for males in this class go up from the male Mean exam score to _______ points.

Choose from the following options:

33.7, 35.1, 34, 34.0, 121.5

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5) On average, grades for males in class go down from the male Mean exam score to ______ points.

Choose from the following options:

4.9, 23, 22.5, 23.9, 24.9

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6) Which of the following six statements is correct?

Choose from the following choices:

a) There is no meaningful difference in grades between female and male students on this exam. We can tell this because the Mean scores are not very different between females and males.

b) Female students did meaningfully better on this exam than male students. We can tell this because the Mean grade for females was higher than the Mean grade for males.

c) Female students did meaningfully better on this exam than male students. We can tell this because the Average Deviation in grades for females is a smaller number than the Average Deviation in grades for males.

d) Female students did meaningfully better on this exam than male students. We can tell this because the Average Deviation in grades for females went higher on the Figure than the Average Deviation in grades for males.

e) Male students did meaningfully better on this exam than female students. We can tell this because the Average Deviation in grades for males is a larger number than the Average Deviation in grades for females.

f) There is no meaningful difference in grades between female and male students on this exam. We can tell this because the Average Deviation lines of female and male students overlap by a large amount.

Answer 1

1)

Female	|(X - X̄)|
17	16.41
20	13.41
30	3.41
31	2.41
31	2.41
33.6	0.19
34	0.59
34.5	1.09
35	1.59
35	1.59
35.6	2.19
36	2.59
36	2.59
36	2.59
36	2.59
37	3.59
37	3.59
37.5	4.09
38	4.59
38	4.59

mean of score = 33.41

sum of deviation = 76.1

average deviation = 76.1/ 20 = 3.805

so, On average, grades for females in this class go up from the female Mean exam score = mean + average dev

= 33.41 + 3.80 = 37.2

2)   On average, grades for females in this class go down from the female Mean exam score = mean - average dev

= 33.41 - 3.8 = 29.6

3)

male	|(X - X̄)|
11.5	17.33
21.5	7.33
22.5	6.33
22.5	6.33
23.5	5.33
26	2.83
28	0.83
29	0.17
30.5	1.67
30.5	1.67
30.5	1.67
31	2.17
32	3.17
32.8	3.97
34	5.17
34	5.17
35.4	6.57
36	7.17
36.5	7.67

mean=28.83

sum of dev = 92.57

average = 92.57 / 19 = 4.87 = 4.9

4)

so, On average, grades for males in this class go up from the male Mean exam score = mean + average dev

= 28.8 +4.9 =33.7

5)

so, On average, grades for males in this class go down from the male Mean exam score = mean - average dev

  

= 28.8 -4.9 =23.9

6)

a) FALSE .. AS means are different

b)

TRUE AS MEAN FOR FEMALE = 33.41

MEAN FOR MALE = 28.83

C)

TRUE AS AVERAGE DEV IN FEAMLE IS SMALLER

D)

FALSE AS AVE DEV IS NOT HEIGHER THAN MALE

E)

FALSE..MALE STUDENT DID NOT DO BETTER

F)

FALSE ..THERE ARE MEANINGFUL DIFFERENCES BETWEEN THE MEANS