Find the mean and standard deviation using short-cut method.

Question:

Find the mean and standard deviation using short-cut method.

Solution:

The data is obtained in tabular form as follows.

Mean, $\frac{-}{x}=A \frac{\sum_{i=1}^{9} f_{i} y_{i}}{N} \times h=64+\frac{0}{100} \times 1=64+0=64$

Variance,$\sigma^{2}=\frac{h^{2}}{N^{2}}\left[N \sum_{i=1}^{9} f_{i} y_{i}^{2}-\left(\sum_{i=1}^{9} f_{i} y_{i}\right)^{2}\right]$

$=\frac{1}{100^{2}}[100 \times 286-0]$

$=2.86$

$\therefore$ Stan dard deviation $(\sigma)=\sqrt{2.86}=1.69$

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