1. 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
a. What is the mean age of this sample? What is the standard deviation?
b. Create a frequency distribution table for denomination.
c. What is the percentage of people who identify themselves as Baptist in this sample?
d. What is the mode of church attendance?
a. To calculate the mean and standard deviation of age in this sample, you can follow these steps:
1. Add up all the ages: 56 + 46 + 49 + 49 + 27 + 51 + 47 + 67 + 49 + 33 + 55 + 40 + 62 + 47 + 56 + 22 + 50 + 51 + 50 + 43 = 965.
2. Divide the sum by the number of people in the sample (20): 965 / 20 = 48.25. This is the mean age of the sample.
3. Calculate the squared deviations from the mean for each age: (56 - 48.25)^2, (46 - 48.25)^2, (49 - 48.25)^2, and so on for each age. Then sum up all these squared deviations: 144.6875 + 6.6875 + 0.5625 + ... (continuing for all 20 numbers) = sum of squared deviations.
4. Divide the sum of squared deviations by the number of people in the sample (20): sum of squared deviations / 20 = variance.
5. Take the square root of the variance to get the standard deviation. This gives us the final answer.
b. To create a frequency distribution table for denomination, follow these steps:
1. List all the possible denominations.
2. Count how many people in the sample identify with each denomination.
3. Create a table with two columns: one for the denominations and the other for the frequencies (counts).
4. Fill in the table with each denomination and its corresponding frequency.
c. To calculate the percentage of people who identify themselves as Baptist in this sample:
1. Count how many people from the sample identify themselves as Baptist.
2. Divide this count by the total number of people in the sample (20).
3. Multiply the result by 100 to get the percentage.
d. To find the mode of church attendance:
1. Count how many people in the sample have each level of church attendance (less than once a month, once a month, etc.).
2. Identify the level(s) of church attendance with the highest count - these will be the mode(s).