The standard deviation exists as the positive square root of the variance.
So, the standard deviation = 6.819.
<h3>How to estimate the standard deviation?</h3>
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 ![$=\frac{15+17+23+5+21+19+26+4+14}{9}](https://tex.z-dn.net/?f=%24%3D%5Cfrac%7B15%2B17%2B23%2B5%2B21%2B19%2B26%2B4%2B14%7D%7B9%7D)
Mean ![$=\frac{144}{9}](https://tex.z-dn.net/?f=%24%3D%5Cfrac%7B144%7D%7B9%7D)
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 ![$=\frac{1+ 1+14+ 121+25+ 9+ 100+ 144+ 4}{9}](https://tex.z-dn.net/?f=%24%3D%5Cfrac%7B1%2B%201%2B14%2B%20121%2B25%2B%209%2B%20100%2B%20144%2B%204%7D%7B9%7D)
Variance ![$=\frac{419}{9}](https://tex.z-dn.net/?f=%24%3D%5Cfrac%7B419%7D%7B9%7D)
Variance = 46.5
The standard deviation exists as the positive square root of the variance.
so, the standard deviation
.
To learn more about standard deviation refer to:
brainly.com/question/475676
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