Question

I need to compute the standard deviation using the correct formula.

Answer 1

To find the standard deviation:

From the given table values,

Sum of the squared deviation is,

222.6064+166.9264+119.2464+98.4064+98.4064+79.5664+35.0464+8.5264+

3.6864+3.6864+0.8464+0.8464+0.0064+0.0064+0.0064+0.0064+4.3264+

4.3264+82.4464+82.4464+101.6064+145.9264+145.9264+145.9264+121.0864=1671.84.

The formula for standard deviation is,

`\sigma=\sqrt[]{\frac{\sum^{}_{}(x-\mu)^2}{N}}`

Here, N=25

So we have,

`\begin{gathered} \sigma=\sqrt[]{(1671.84)/(25)} \\ =\sqrt[]{66.8736} \\ =8.1776 \end{gathered}`

Hence the standard deviation is,

`\sigma=8.1776`