Mathematics: Find the standard deviation for the following group of data items. 9, 11, 11, 16

1/3 * 44/3 or 1 1/3 4/3 or 1 1/3...

Find the standard deviation for the following

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26.08.2021

The standard deviation for the given data items is 2.6

The standard deviation of the given data items can be calculated by taking the square root of the variance.

Variance is a measure of variability and it is calculated by taking the average of squared deviations from the mean.

Hence, we will first determine the mean of the given data items.

Mean is simply the average of the numbers.

Therefore mean of the given data items is

$Mean = \frac{9+11+11+16}{4}$

$Mean = \frac{47}{4}$

Mean = 11.75

Now, for the variance of the data

$Variance = \frac{(9-11.75)^{2}+(11-11.75)^{2}+(11-11.75)^{2}+(16-11.75)^{2} }{4}$

$Variance = \frac{(-2.75)^{2}+(-0.75)^{2}+(-0.75)^{2}+(4.25)^{2} }{4}$

$Variance = \frac{7.5625+0.5625+0.5625+18.0625}{4}$

$Variance = \frac{26.75}{4}\\$

∴ Variance = 6.6875

But,

Standard deviation $= \sqrt{Varinace}$

∴Standard deviation $=\sqrt{6.6875}$

Standard deviation = 2.586

Standard deviation ≅ 2.6

Hence, the standard deviation for the given data items is 2.6

Learn more on standard deviation here:

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