the prison popuation of 9 different countries are: 50, 30, 10, 50, 60, 50, 20, 40, 50. What is the range and standard deviation? Explain.

I know the range is 50, but i cant figure out the standard deviation.

To calculate the standard deviation of a set of data, you need to follow these steps:

Step 1: Calculate the mean (average) of the data set.
Step 2: Subtract the mean from each value to get the deviation from the mean.
Step 3: Square each deviation.
Step 4: Find the average of these squared deviations (mean of squared deviations).
Step 5: Take the square root of the mean of squared deviations to get the standard deviation.

Now let's calculate the standard deviation for the given data set:

1. Calculate the mean:
Mean = (50 + 30 + 10 + 50 + 60 + 50 + 20 + 40 + 50) / 9
= 360 / 9
= 40

2. Calculate the deviation from the mean for each value:
Deviations from the mean: (50 - 40), (30 - 40), (10 - 40), (50 - 40), (60 - 40), (50 - 40), (20 - 40), (40 - 40), (50 - 40)
= 10, -10, -30, 10, 20, 10, -20, 0, 10

3. Square each deviation:
Squared deviations: 10^2, (-10)^2, (-30)^2, 10^2, 20^2, 10^2, (-20)^2, 0^2, 10^2
= 100, 100, 900, 100, 400, 100, 400, 0, 100

4. Find the average of the squared deviations (mean of squared deviations):
Mean of squared deviations = (100 + 100 + 900 + 100 + 400 + 100 + 400 + 0 + 100) / 9
= 2200 / 9
≈ 244.44

5. Take the square root of the mean of squared deviations to get the standard deviation:
Standard Deviation ≈ √244.44
≈ 15.63

Therefore, the standard deviation of the given data set is approximately 15.63.