(b) Use the defining formula to compute the sample standard deviation s_ Recall the defining formula used to compute the sample standard deviation $ where x is a F = member of the data set, x is the mean, and n is number of data values Before using the formula, we must determine x and n There are five values in the data set 1, 2, 4, 7, 8, so n Calculate the mean X by taking the average of the data values, which is dividing the sum of the data values by the number of data values: 1 + 2 + 4 + 7 + 8 22 Step 3 In order to use the defining formula for sample standard deviation, it is helpful to first calculate (x each data value in the data set 1, 2, 4, 7, 8. for Use the values in the data set and the previously determined mean, x = 4.4,to complete the following table_ 4.4 4.4 4.4 4.4 4.4 X-* ~3.4 0.4 3.6 11.56 5.76 6.76 (iX?

A high standard deviation means that values are generally far from the mean, while a low standard deviation indicates that values are clustered close to the mean. The standard deviation and the mean together can tell you where most of the values in your frequency distribution lie if they follow a normal distribution.

Dataset: 1,2,4,7,8

So, n = 5 (because the sample size is 5)

We calculate the mean X by taking the average of the data values, which is dividing the sum of the data values by the number of data values:

X = 1+2+4+7+8/5

X=22/5 = 4.4

So, the average is 4.4

For standard deviation calculation,

$ = [tex]{\sqrt{(x-X)^2/n-1} }[/tex]

Thus, the standard deviation is 4.95.

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