# Applied Research Methods

Review DESCRIPTIVE STATISTICS CASE STUDY and answer the 26 questions.

DESCRIPTIVE STATISTICS CASE STUDY:

The four variables shown in the data set below are set up to represent a fictitious
study of gender, weight and fitness score. The variables include gender, ranking, weight
and score. In this example, gender is coded as m or f (recoded as 1 or 2 for
computations), weight is the participant’s weight, score is a value that the participant
scored in a fitness test and rank is their ranking based on that score.

Gender Ranking Weight Score

m 1 200 95
m 2 110 92
f 3 103 91
f 4 145 90
f 5 130 88
m 6 180 82
m 7 170 80
f 8 90 75
f 9 102 70
m 10 225 60
m 11 225 59
m 12 108 55
f 13 108 55
m 14 108 55
m 15 167 50

EACH OF THE VARIABLES IS EXAMINED IN THE CHART BELOW:

Statistics

GENDER RANKING SCORE WEIGHT
N Valid
Missing

Statistic
Statistic

15
0

15
0
15
0
15
0

Mean Statistic
St. Error

1.40
.13

8.0000
1.1547

73.1333
4.1928

144.7333
12.0224

Median Statistic 1.00 8.0000 75.0000 130.0000
Mode Statistic 1 1.00 a 55.00 108.00
Std. Deviation Statistic .51 4.4721 16.2387 46.5625
Variance Statistic .26 20.0000 263.6952 2168.0667
Skewness Statistic

St. Error
.455
.580

.000

.580
-.065
.580

.625

.580
Kurtosis Statistic

St. Error
-2.094
1.121

-1.200
1.121

-1.753
1.121

-1.037
1.121

Range Statistic 1 14.00 45.00 135.00
Minimum Statistic 1 1.00 50.00 90.00
Maximum Statistic 2 15.00 95.00 225.00

a. Multiple modes exist. The smallest value is shown

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YOUR TURN Using the values from the GENDER variable in table above, answer the
following questions.
===============================================================

1. What type of data does gender represent?

2. What does the mean gender of 1.40 tell us?

3. What would be the appropriate measure of central tendency for GENDER?

4. What is the value for central tendency?

===============================================================
YOUR TURN Using the values from the RANKING variable in table above, answer the
following questions.

5. What type of data does RANKING represent?

6. What is the appropriate measure of central tendency?

7. What is the value for central tendency?

8. Would it be appropriate to describe the average ranking? Why or why not?

===============================================================
YOUR TURN Using the values from the SCORE variable in the table above, answer the
following questions.

9. What type of data does SCORE represent?

10. What is the mean, median and mode of this data set?

11. What does the difference between the mean, median and mode tell you?

12. Is this data set skewed? If so, in which direction?

13. What is the range of the data set? How is this determined?

14. What does the kurtosis figure tell you?

15. Do you think this data is normally distributed? Why?

16. What does the standard error tell you?

17. What is the relationship between the variance and the standard deviation? What do
these numbers tell you?

===============================================================
YOUR TURN Using the values from the WEIGHT variable in the table above, answer
the following questions.
===============================================================

18. What type of data does WEIGHT represent?

19. What is the mean, median and mode of this data set?

20. What does the difference between the mean, median and mode tell you?

21. Is this data set skewed? If so, in which direction?

22. What is the range of the data set? How is this determined?

23. What does the kurtosis figure tell you?

24. Do you think this data is normally distributed? Why?

25. What does the standard error tell you?

26. What is the relationship between the variance and the standard deviation? What do
these numbers tell you?