For the following set of data, find the population standard deviation, to the nearest thousandth.

45, 30, 35, 20, 21, 46, 16, 37

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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.

a) is $10.34

b) is 6 toppings

the anwser is x< -17/2