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Find the mean and variance for the data

Question:

Find the mean and variance for the data

Solution:

The data is obtained in tabular form as follows.

Here, $N=22, \sum_{i=1}^{7} f_{i} x_{i}=2200$

$\therefore \bar{x}=\frac{1}{N} \sum_{i=1}^{7} f_{i} x_{i}=\frac{1}{22} \times 2200=100$

Variance $\left(\sigma^{2}\right)=\frac{1}{N} \sum_{i=1}^{7} \mathrm{f}_{i}\left(\mathrm{x}_{i}-\overline{\mathrm{x}}\right)^{2}=\frac{1}{22} \times 640=29.09$

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