Question

The ages of all employees at a small convenience store are 38, 26, 42, and 22. What is standard deviation of ages for this population? Select one:

a. 90.67
b. 68.00
c. 8.25
d. 9.52

Answer 1

To calculate the standard deviation of the ages of employees at the convenience store, we find the mean age, compute the variance by averaging the squared differences from the mean, and then take the square root of the variance. The correct standard deviation is approximately 8.25.

Step-by-step explanation:

To calculate the standard deviation of the ages for the population of employees at the convenience store, we first need to find the mean (average) age. The mean age is calculated by adding all the ages together and dividing by the number of employees. So, we have:

(38 + 26 + 42 + 22) / 4 = 128 / 4 = 32

Now that we have the mean age, we can calculate the variance. We do this by subtracting the mean from each age, squaring the result, and then taking the average of these squared differences. This gives us:

[(38 - 32)^2 + (26 - 32)^2 + (42 - 32)^2 + (22 - 32)^2] / 4

=(36 + 36 + 100 + 100) / 4

= 272 / 4

= 68

The variance of the employees' ages is 68. The standard deviation is the square root of the variance, so:

standard deviation = √68 ≈ 8.25

Therefore, the correct answer is c. 8.25.