. A graduate student has collected data involving 66 scores. Based on these data, he has constructed two frequency distributions of grouped scores. These are shown here. Do you see anything wrong with these distributions? Explain.

Class Interval f

48-63 17

29-47 28

10-28 21

Class Interval f Class Interval f

62-63 2 34-35 2

60-61 4 32-33 0

58-59 3 30-31 5

56-57 1 28-29 3

54-55 0 26-27 0

52-53 4 24-25 4

50-51 5 22-23 5

48-49 2 20-21 2

46-47 0 18-19 0

44-45 5 16-17 3

42-43 4 14-15 1

40-41 3 12-13 0

38-39 0 10-11 2

4. The following scores show the amount of weight lost (in pounds) by each client of a weight control

clinic during the last year:

10 13 22 26 16 23 35 53 17 32 41 35 24 23 27 16 20 60 48 43 52 31 17 20 33 18 23 8 24 15 26 46

30 19 22 13 22 14 21 39 28 43 37 15 20 11 25 9 15 21 21 25 34 10 23 29 28 18 17 24 16 26 7 12

28 20 36 16 14 18 16 57 31 34 28 42 19 26

a. Construct a frequency distribution of grouped scores with approximately 10 intervals.

b. Construct a histogram of the frequency distribution constructed in part a.

c. Is the distribution skewed or symmetrical? If it is skewed, is it skewed positively or negatively?

d. Construct a stem and leaf diagram with the last digit being a leaf and the first digit a stem.

e. Which diagram do you like better, the histogram of part b or the stem and leaf diagram of part d?

Explain.

5. Convert the grouped frequency distribution of weight losses determined in Problem 4 to a relative

frequency and a cumulative frequency distribution.

6. Using the cumulative frequency distribution arrived at in Problem 5, determine,

a. The percentile rank of a score of 41

b. The percentile rank of a score of 28 clinical