Statistics I for Educational Services Essay

NAME(S): ____________________________________________________________________

Multiple Choice:

Please circle either A, B, C, or D.

1. (1 Point) A classroom test given to sixth graders tends to have a large number of high

scores. The distribution would be…

A. symmetric.

B. positively skewed.

C. negatively skewed.

D. platykurtic.

2. (1 Point) Twenty-five different bands/singers participated in a massive concert. In the

September issue of Rolling Stone magazine, the bands were rated 1 (i.e., Poor), 2 (i.e.,

Fair), 3 (i.e., Good), or 4 (i.e., Excellent). This is an example of what kind of

measurement?

A. Nominal

B. Ordinal

C. Interval

D. Ratio

Statistics I for Educational Services Essay

3. (1 Point) John’s percentile rank for his score of 84 on a science test was 78%. This means

that…

A. John answered 78% of the items correctly.

B. 78% of the scores on a science test fell below John’s score of 84.

C. John answered 78 items correctly.

D. John was below average on the science test.

4. (1 Point) Which of the following is not a continuous variable?

A. Time to solve a problem.

B. Temperature.

C. Height.

D. Number of children in a family.

2

5. (1 Point) A distribution is positively skewed. Which is the most probable order for the

three measures of central tendency?

A. Mean = 40, median = 50, mode = 60

B. Mean = 60, median = 50, mode = 40

C. Mean = 40, median = 60, mode = 50

D. Mean = 50, median = 50, mode = 50

True/False:

Please write either “T” for True or “F” for False. If False, indicate WHY it is false, and

correct the statement to make it True.

6. (.25 Points) A distribution can have more than one mean.

7. (.25 Points) A distribution can have more than one mode.

8. (.25 Points) For any symmetrical distribution the mean is equal to the median.

9. (.25 Points) A researcher interested in human memory selects a group of 30 students to

participate in a research study. The group of 30 students would be considered a

population.

10. (.25 Points) Extreme scores in a distribution are more likely to affect the value of the

mean than the value of the median.

11. (.25 Points) The symbol of σ 2 stands for the sample variance.

3

12. (.25 Points) The interval of 25 – 29 has real limits of 24.5 and 29.5.

13. (.25 Points) If a score, X = 30, has a percentile rank of 90%, then 90% of the scores in the

distribution will have a value equal to 30.

14. (.25 Points) To compute ΣX 2 , you first sum the scores and then square the total.

15. (.25 Points) Last week, the three major networks were ranked as follows: (1) NBC, (2)

CBS, and (3) ABC. This is an example of measurement on a nominal scale.

Short Answer:

Please indicate if the variable in question is: (1) Qualitative or Quantitative, (2) Discrete or

Continuous, and (3) Nominal, Ordinal, Interval, or Ratio. Use the space under each

variable to explain or justify your choices, if needed. There may be more than one correct

answer.

Statistics I for Educational Services Essay

Variable Qualitative or

Quantitative

Discrete or

Continuous

Level of

Measurement

16. (1 Point) Customer Satisfaction (Likert)

17. (1 Point) Hours of Sleep Last Night

4

18. (1 Point) Math Ability (e.g., GRE)

19. (1 Point) Religious Affiliation

20. (1 Point) End-of-Course Letter Grade

21. (1 Point) What are the main differences between a bar graph and a histogram?

22. (1 Point) What is the problem with using deviation scores as a measure of dispersion to

describe a set of data?

5

Computational:

Find each of the requested values (below) for the distribution shown in the following table.

Pay attention to the interval width (i.e., URL – LRL)! Round to two decimal places. Show

your work.

X f cf crf

55-59 1 25 100

50-54 2 24 96

45-49 2 22 88

40-44 2 20 80

35-39 4 18 72

30-34 5 14 56

25-29 2 9 36

20-24 4 7 28

15-19 2 3 12

10-14 1 1 4

23. (.5 Points) What score is associated with the 50 th percentile?

24. (.5 Points) What score is associated with the 25 th percentile?

25. (.5 Points) What score is associated with the 75 th percentile?

26. (.5 Points) What is the Interquartile Range?

27. (.5 Points) What is the shape of the distribution (e.g., symmetric, positively, or negatively

skewed) based on the above calculated quartiles? Show your calculations.

Statistics I for Educational Services Essay

6

Here is a data set of 50 scores.

141 87 115 91 96 92 118 98 101 107

97 124 118 146 108 106 135 97 108 129

107 110 101 129 109 83 127 116 113 105

127 114 112 114 139 109 102 113 106 89

108 92 102 102 134 104 101 131 86 123

28. (1 Point) Use the seven rows below to create a Grouped Frequency Distribution (i.e., w = 10)

and a Relative Frequency Distribution with the above data set. Round to two decimal places.

The first row is set up for you.

Interval (X) f rf

140-149 2 .04

29. (1 Point) Determine the Lower and

Upper Real Limits for each interval from

the above data. Determine the

Cumulative Relative Frequency

Distribution. Round to two decimal

places. The first row is set up for you.

Real Limits crf

139.5-149.5 1.00 (100%)

Statistics I for Educational Services Essay

7

30. (1 Point) Using the Real Limits from the above data set, create an ogive curve (i.e.,

Cumulative Frequency Polygon). Remember the rules for creating an ogive curve!

31. (.5 Points) From the above give curve that you created, what score is located at the 80 th

percentile?