The salaries (in thousands of dollars) for a sample of 13 employees of a firm are: 26.5, 23.5, 29.7, 24.8, 21.1, 24.3, 20.4, 22.7, 27.2, 23.7, 24.1, 24.8, and 28.2.
Compute the variance of the salaries.
a)2.562
b)6.125 - I Picked this
c)9.223
d)7.097
Your pick is incorrect. It's either c) or d). Remember that standard deviation is the square root of the variance, and variance is standard deviation squared.
To compute the variance of the salaries, you can follow these steps:
1. Find the mean: Add up all the salaries and divide by the number of employees.
Sum = 26.5 + 23.5 + 29.7 + 24.8 + 21.1 + 24.3 + 20.4 + 22.7 + 27.2 + 23.7 + 24.1 + 24.8 + 28.2 = 310.1
Mean = Sum / Number of employees = 310.1 / 13 = 23.854
2. Subtract the mean from each salary and square the result:
(26.5 - 23.854)^2 = 6.956996
(23.5 - 23.854)^2 = 0.126916
(29.7 - 23.854)^2 = 34.343716
(24.8 - 23.854)^2 = 0.896996
(21.1 - 23.854)^2 = 7.640676
(24.3 - 23.854)^2 = 0.199156
(20.4 - 23.854)^2 = 11.903516
(22.7 - 23.854)^2 = 1.326996
(27.2 - 23.854)^2 = 10.538736
(23.7 - 23.854)^2 = 0.022596
(24.1 - 23.854)^2 = 0.059616
(24.8 - 23.854)^2 = 0.896996
(28.2 - 23.854)^2 = 18.656496
3. Calculate the sum of all the squared differences:
Sum of squared differences = 6.956996 + 0.126916 + 34.343716 + 0.896996 + 7.640676 + 0.199156 + 11.903516 + 1.326996 + 10.538736 + 0.022596 + 0.059616 + 0.896996 + 18.656496 = 92.843136
4. Divide the sum of squared differences by the number of employees minus 1 to get the variance:
Variance = Sum of squared differences / (Number of employees - 1) = 92.843136 / (13 - 1) = 92.843136 / 12 ≈ 7.736928
So, the variance of the salaries is approximately 7.736928, which is closest to option d) 7.097.