# Frequency Distributions

Frequency Distributions

The following are 50 scores on a History examination.

37

39

42

30

38

20

17

16

15

6

25

22

15

25

31

18

21

13

5

11

27

26

26

22

31

15

16

22

17

6

22

27

27

32

17

32

14

12

23

18

28

29

33

28

19

19

34

20

21

29

From these scores, construct a frequency distribution table.

Use nine classes, with the first class 0–4, and the last 40–44

Class Interval

tally

frequency

40-44

1. (_____)_

35-39

2. (_____)_

30-34

3. (_____)_

25-29

4. (_____)_

20-24

5. (_____)_

15-19

6. (_____)_

10-14

7. (_____)_

5-9

8. (_____)_

1.4 ___

9. (_____)_

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EDUC 606

II.

From the following scores on two tests, calculate the following values:

Test 1 (X): 29, 28, 25, 25, 22, 22, 21, 20, 19, 19

Test 2 (Y): 34, 31, 35, 30, 31, 28, 28, 25, 24, 24

Mean of Test 1 (X)

10. Mx= (_____)

Mean of Test 2 (Y)

11. My= (____)

12. Summation of squared deviations scores for Test 1

Σx2= (______)

Summation of squared deviations scores for Test 2

13. Σy2 = (______)

Summation of the product of deviation scores for Test 1 and Test 2

14. Σxy = (______)

Correlation Coefficient:

15. r = (_____)

III.

Twenty students received the following scores on a short quiz:

23, 20, 20, 19, 19, 19, 18, 18, 18, 18,

17, 17, 17, 15, 14, 13, 13, 12, 12, 18.

Calculate the following:

16. Mean= (______)

17. Median=(______)

18. Mode= (______)

19. SD =

(______)

20. If this small sample is normally distributed, 68% of the scores should fall

between what two values? ______________and___________________.

IV.

A student takes examinations in a History course and an English course.

The following information is taken from the two tests:

Page 2 of 5

EDUC 606

History

64

54

4

Student Score

Mean

SD

English

80

70

10

21. What is the z-score for History? (_______)

22. What is the z-score for English? (_______)

23. What is the T-score for History? (_______)

24. What is the T-score for English? (_______)

V. Use the following data to answer questions 25 – 30. (*indicates the correct answer).

ITEM 1

A

B

C

D*

ITEM 2

A

B

C*

D

UPPER

2

4

2

4

UPPER

0

5

5

5

LOWER

6

1

3

2

LOWER

0

3

11

1

Circle the letter of the correct answer.

25. What is the difficulty level of item 1?

26. What is the difficulty level of item 2?

a. 4/12

a. 5/15

b. 6/12

b. 6/15

c. 2/24

c. 5/30

d. 4/24

d. 6/30

e. 6/24

e. 16/30

27. What is the discrimination index of item 1?

28. What is item 2’s discrimination index?

a. 2/12

a. 6/15

b. 6/12

b. 4/15

c. 2/24

c. -6/15

d. 6/24

d. -6/30

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EDUC 606

29. Which distractor on Item 1 needs revision or elimination?

a. 1-A

b. 1-B

c. 1-C

d. None of these

30. Which of the following is indicated by Item 2?

a. Ambiguous

b. Guessing

c. Miskeyed

d. Too difficult

31. The majority of Mr. Smith’s students made very high scores on this test. The curve of

the distribution of scores on this test would most likely be

a. normal

b. symmetrical

c. positively skewed

d. negatively skewed

32. Which of the following r’s have the least predictive value?

a. 0.91

b. 0.50

c. 0.17

d. 0.23

e. -1.00

33. The reliability procedure that involves correlation of partial scores from one