For the following set of data, find the population standard deviation, to the nearest thousandth.
101, 79, 117, 99, 96, 112, 87, 75
To find the population standard deviation, we first need to find the mean of the data set:
Mean = (101 + 79 + 117 + 99 + 96 + 112 + 87 + 75) / 8
Mean = 866 / 8
Mean = 108.25
Next, we need to find the squared difference between each data point and the mean:
(101 - 108.25)^2 = 53.0625
(79 - 108.25)^2 = 852.5625
(117 - 108.25)^2 = 76.5625
(99 - 108.25)^2 = 85.5625
(96 - 108.25)^2 = 149.0625
(112 - 108.25)^2 = 14.0625
(87 - 108.25)^2 = 454.0625
(75 - 108.25)^2 = 1104.0625
Now, find the sum of these squared differences:
53.0625 + 852.5625 + 76.5625 + 85.5625 + 149.0625 + 14.0625 + 454.0625 + 1104.0625 = 2794.9375
Next, divide this sum by the total number of values in the data set (8) to get the variance:
Variance = 2794.9375 / 8
Variance = 349.3671875
Finally, take the square root of the variance to get the population standard deviation:
Population Standard Deviation = √349.3671875
Population Standard Deviation ≈ 18.68
Therefore, the population standard deviation for the given data set is approximately 18.68, rounded to the nearest thousandth.