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Explanation:
Before we can find the standard deviation, we need to find the sample mean which is xbar.
Xbar is found by adding up the values and dividing by n = 8 since there are 8 values in this data set
xbar = (sum of values)/n
xbar = (45+30+35+20+21+46+16+37)/8
xbar = 31.25
Refer to the spreadsheet table below in the attached image. The first column is the column of x values, which is the data set given to us. The next column over is the expression x-xbar, which will have us subtract xbar from each data value.
Example: x-xbar = 30-31.25 = -1.25 in row 2
From there, we square everything in that second column to form the third column. Adding everything in that third column results in the yellow highlighted value 919.5
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The next step is to divide that over n = 8 to get 919.5/n = 919.5/8 = 114.9375
This is the population variance. Apply the square root to get the population standard deviation
sqrt(variance) = sqrt(114.9375) = 10.7208908
which is approximate. This rounds to 10.721
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Note: if you wanted the sample standard deviation, then you'd divide by n-1 = 8-1 = 7. However, the other steps mentioned are identical.
