For the frequency distribution:
Question:

For the frequency distribution:

Find the standard distribution.

Solution:

Given frequency distribution table

Now we have to find the standard deviation

Let us make a table of the given data and append other columns after calculations

And we know standard deviation is

$\sigma=\sqrt{\frac{\sum f_{i} x_{i}^{2}}{n}-\left(\frac{\sum f_{i} x_{i}}{n}\right)^{2}}$

Substituting values from above table, we get

$\sigma=\sqrt{\frac{1393}{60}-\left(\frac{277}{60}\right)^{2}}$

$\sigma=\sqrt{23.23-(4.62)^{2}}$

 

$\sigma=\sqrt{23.23-21.34}$

$\Rightarrow \sigma=1.37$

Hence the standard deviation is $1.37 .$

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