For the following set of data, find the population standard deviation, to the nearest thousandth.
110, 99, 52, 45, 109, 108, 68, 89, 116
Step 1: Find the mean of the data set
Mean = (110 + 99 + 52 + 45 + 109 + 108 + 68 + 89 + 116) / 9
Mean = 796 / 9
Mean = 88.444
Step 2: Find the squared difference of each data point from the mean
(110 - 88.444)^2 = 476.076
(99 - 88.444)^2 = 111.798
(52 - 88.444)^2 = 1327.219
(45 - 88.444)^2 = 1884.193
(109 - 88.444)^2 = 424.149
(108 - 88.444)^2 = 381.431
(68 - 88.444)^2 = 413.117
(89 - 88.444)^2 = 0.245
(116 - 88.444)^2 = 760.509
Step 3: Find the sum of the squared differences
Sum of squared differences = 476.076 + 111.798 + 1327.219 + 1884.193 + 424.149 + 381.431 + 413.117 + 0.245 + 760.509
Sum of squared differences = 5378.737
Step 4: Find the variance
Variance = Sum of squared differences / N
Variance = 5378.737 / 9
Variance = 597.637
Step 5: Find the population standard deviation
Population standard deviation = square root of the variance
Population standard deviation ≈ √597.637
Population standard deviation ≈ 24.458
Therefore, the population standard deviation of the data set is approximately 24.458.