To help study neighborhood demographics, a community organization conducts a survey of 10 neighborhood residents, asking each one how many children under 18 live in their household. The responses are given below.

Question

0, 0, 0, 7, 0, 2, 0, 0, 2, 2

What are the mean and standard deviation of this data set?
Mean: 1.30, Standard Deviation: 2.21
Mean: 2.21, Standard Deviation: 1.30
Mean: 0.00, Standard Deviation: 2.00
Mean: 3.50, Standard Deviation: 7.00
Mean: 1.30, Standard Deviation: 4.90

Answer 1

Mean: 1.30, Standard Deviation: 2.21

To calculate the mean, add up all the values and divide by the total number of values:
Mean = (0 + 0 + 0 + 7 + 0 + 2 + 0 + 0 + 2 + 2) / 10 = 13 / 10 = 1.30

To calculate the standard deviation, first find the variance by following these steps:
1. Find the difference between each value and the mean, then square the result.
2. Find the average of these squared differences.
3. Take the square root of the result from step 2 to get the standard deviation.

The squared differences from the mean for each value are:
(0-1.30)^2 = 1.69, (0-1.30)^2 = 1.69, (0-1.30)^2 = 1.69, (7-1.30)^2 = 32.49, (0-1.30)^2 = 1.69, (2-1.30)^2 = 0.49, (0-1.30)^2 = 1.69, (0-1.30)^2 = 1.69, (2-1.30)^2 = 0.49, (2-1.30)^2 = 0.49

The average of these squared differences is: (1.69 + 1.69 + 1.69 + 32.49 + 1.69 + 0.49 + 1.69 + 1.69 + 0.49 + 0.49) / 10 = 40.9 / 10 = 4.09

The standard deviation is the square root of the variance, so:
Standard Deviation = √4.09 ≈ 2.21

Therefore, the mean is 1.30 and the standard deviation is 2.21. So the answer is:
Mean: 1.30, Standard Deviation: 2.21