Question

What is the method for finding the population standard deviation of the given set of numbers: 5, 5, 5, 6, 6, 6, 6, 6, 7?

Answer 1

To find the population standard deviation, you need to find the mean of the set and then calculate the squared differences from the mean for each number. The sum of the squared differences is divided by the total number of numbers, and the square root of that result gives you the population standard deviation.

Step-by-step explanation:

To find the population standard deviation of a given set of numbers, you can follow these steps:

1. Find the mean of the set by adding up all the numbers and dividing by the total number of numbers.
2. Subtract the mean from each number in the set, then square the result.
3. Find the sum of all the squared differences.
4. Divide the sum by the total number of numbers in the set.
5. Take the square root of the result to find the population standard deviation.

For example, to find the population standard deviation of the set {5, 5, 5, 6, 6, 6, 6, 6, 7}, you would follow these steps:

1. Mean = (5+5+5+6+6+6+6+6+7) / 9 = 54 / 9 = 6
2. (5-6)^2 = 1
3. (5-6)^2 = 1
4. (5-6)^2 = 1
5. (6-6)^2 = 0
6. (6-6)^2 = 0
7. (6-6)^2 = 0
8. (6-6)^2 = 0
9. (7-6)^2 = 1
10. Sum = 1+1+1+0+0+0+0+0+1=4
11. Population standard deviation = sqrt(4/9) ≈ 0.67