Q. For the following set of data, find the population standard deviation, to the nearest thousandth.103,107,124,121,123,67,77,107,124
List data set: List the data set and verify the number of data points.The data set given is: 103,107,124,121,123,67,77,107,124.Count the number of data points to ensure none are missing.There are 9 data points in total.
Calculate mean: Calculate the mean (average) of the data set.The mean is calculated by adding all the data points together and then dividing by the number of data points.Mean = (103+107+124+121+123+67+77+107+124)/9Mean = 953/9Mean = 105.888…
Subtract and square: Subtract the mean from each data point and square the result.This step is part of calculating the variance, which is the average of the squared differences from the Mean.(103−105.888)2=8.3472=69.672(107−105.888)2=1.1122=1.237(124−105.888)2=18.1122=328.045(121−105.888)2=15.1122=228.472(123−105.888)2=17.1122=292.922(67−105.888)2=−38.8882=1511.111(77−105.888)2=−28.8882=834.672(107−105.888)2=1.1122=1.237(124−105.888)2=18.1122=328.045
Sum squared differences: Sum the squared differences.Add all the squared differences together to get the total sum.Total sum = 69.672+1.237+328.045+228.472+292.922+1511.111+834.672+1.237+328.045Total sum = 3595.413
Calculate variance: Calculate the variance.Since we are dealing with a population standard deviation, we divide the total sum of squared differences by the number of data points N.Variance=NTotal sumVariance=93595.413Variance=399.490
Calculate standard deviation: Calculate the population standard deviation.The standard deviation is the square root of the variance.Standard deviation = VarianceStandard deviation = 399.490Standard deviation ≈19.987
Round standard deviation: Round the standard deviation to the nearest thousandth.The standard deviation rounded to the nearest thousandth is 19.987.