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Find the standard deviation for the set of data. {15,17,23,5,21,19,26,4,14} a. 7.17 b. 7.39 c. 7.1 d. 6.65

Sagot :

The standard deviation exists as the positive square root of the variance.

So, the standard deviation = 6.819.

How to estimate the standard deviation?

Given data set: 15, 17, 23, 5, 21, 19, 26, 4, 14

To calculate the mean of the data.

We know that mean exists as the average of the data values and exists estimated as:

Mean [tex]$=\frac{15+17+23+5+21+19+26+4+14}{9}[/tex]

Mean [tex]$=\frac{144}{9}[/tex]

Mean = 16

To estimate the difference of each data point from the mean as:

Deviation:

15 - 16 = -1

17 - 16 = 1

23 - 16 = 7

5 - 16 = -11

21 - 16 = 5

19 - 16 = 3

26 - 16 = 10

4 - 16 = -12

14 - 16 = -2

Now we have to square the above deviations we obtain:

1 , 1, 14, 121, 25, 9, 100, 144, 4

To estimate the variance of the above sets:

variance [tex]$=\frac{1+ 1+14+ 121+25+ 9+ 100+ 144+ 4}{9}[/tex]

Variance [tex]$=\frac{419}{9}[/tex]

Variance = 46.5

The standard deviation exists as the positive square root of the variance.

so, the standard deviation [tex]$\sqrt{46.5} =6.819[/tex] .

To learn more about standard deviation refer to:

brainly.com/question/475676

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