Descriptive Statistics Exercises

I. Answer the following questions using the table and data below:
a. What is the mean age of this sample? What is the standard deviation?
b. Create a frequency distribution table for denomination.

Denomination
Frequency Percent Valid Percent Cumulative Percent
Valid Episcopal 1 5.0 5.0 5.0
Lutheran 2 10.0 10.0 15.0
Presbyterian 2 10.0 10.0 25.0
Other Mainline Protestant 1 5.0 5.0 30.0
Baptist 3 15.0 15.0 45.0
Other Evangelical Protestant 3 15.0 15.0 60.0
Pentecostal 1 5.0 5.0 65.0
Charismatic 3 15.0 15.0 80.0
Non-Denominational 3 15.0 15.0 95.0
Other 1 5.0 5.0 100.0
Total 20 100.0 100.0
c. What is the percentage of people who identify themselves as Baptist in this sample?
d. What is the mode of church attendance?
The mode of church attendance is 5, twice a week.
The table below presents data for a sample of people who completed a religious survey.
Age Gender Denomination Church Attendance
56 1 7 4
46 2 6 5
49 2 6 5
49 1 1 5
27 2 9 5
51 1 4 2
47 2 2 3
67 1 5 4
49 2 2 6
33 1 12 6
55 2 9 5
40 1 7 5
62 1 8 6
47 2 6 3
56 2 9 5
22 1 10 2
50 2 4 5
51 1 10 6
50 1 7 6
43 1 10 3
In this table, the numbers in the gender, denomination, and church attendance columns represent the following:
Gender
1. Male
2. Female
Denomination
1. Episcopal
2. Lutheran
3. Methodist
4. Presbyterian
5. Other Mainline Protestant
6. Baptist
7. Other Evangelical Protestant
8. Pentecostal
9. Charismatic
10. Non-Denominational
11. Catholic
12. Other
Church Attendance
1. Less than once a month
2. Once a month
3. A few times a month
4. Once a week
5. Twice a week
6. Three or more times a week
II. The results of a recent survey indicate that the average new car costs $23,000, with a standard deviation of $3,500. The price of cars is normally distributed.
a. What is a Z score for a car with a price of $33,000?

b. What is a Z score for a car with a price of $30,000?

c. At what percentile rank is a car that sold for $30,000?

III. In one elementary school, 200 students are tested on the subjects of math and English. The table below shows the mean and standard deviation for each subject.
Subject Mean SD
Math 67 9.58
English 78 12.45
One student's math score was 70 and the same student's English score was 84. On which exam did the student do better?

IV. Suppose you administered an anxiety test to a large sample of people and obtained normally distributed scores with a mean of 45 and a standard deviation of 4. Do not use the web calculator to answer the following questions. Instead, use the Z distribution table below and Appendix A in the Jackson text.
a. If Andrew scored 45 on this test, what is his Z score?

b. If Anna scored 30 on this test, what is her Z score?

c. If Bill's Z score was 1.5, what is his real score on this test?

d. There are 200 students in a sample. How many of these students will have scores that fall under the score of 41?

Caption: The Normal Distribution Curve.
"The Normal Distribution", ©2007, used under a creative commons attribution- Share alike 3.0 unported license with address: http://commons.wikimedia.org/wiki/File:The_Normal_Distribution.svg. Retrieved from: http://commons.wikimedia.org/wiki/File:The_Normal_Distribution.svg.

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