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Find the mean and variance for the following frequency distribution.

Question:

Find the mean and variance for the following frequency distribution.

Solution:

Mean, $\bar{x}=\mathrm{A}+\frac{\sum_{\mathrm{i}=1}^{7} \mathrm{f}_{\mathrm{i}} \mathrm{y}_{\mathrm{i}}}{\mathrm{N}} \times \mathrm{h}=105+\frac{2}{30} \times 30=105+2=107$

$\operatorname{Variance}\left(\sigma^{2}\right)=\frac{h^{2}}{N^{2}}\left[N \sum_{i=1}^{7} f_{i} y_{i}^{2}-\left(\sum_{i=1}^{7} f_{i} y_{i}\right)^{2}\right]$

$=\frac{(30)^{2}}{(30)^{2}}\left[30 \times 76-(2)^{2}\right]$

$=2280-4$

$=2276$

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