# 8.  Find the mean and variance for the following frequency distributions. Classes 0-10 10-20 20-30 30-40 40-50 Frequencies 5 8 15 16 6

 Classes Frequency $f_i$ Mid-point  $x_i$ $f_ix_i$ $(x_i - \overline{x})$ $(x_i - \overline{x})^2$ $f_i(x_i - \overline{x})^2$ 0-10 5 5 25 -22 484 2420 10-20 8 15 120 -12 144 1152 20-30 15 25 375 -2 4 60 30-40 16 35 560 8 64 1024 40-50 6 45 270 18 324 1944 $\sum{f_i}$ = N = 50 $\sum f_ix_i$ = 1350 $\sum f_i(x_i - \overline{x})^2$ =6600

$\overline{x} = \frac{1}{N}\sum_{i=1}^{n}f_ix_i = \frac{1350}{50} = 27$

We know, Variance, $\sigma^2 = \frac{1}{N}\sum_{i=1}^{n}(x_i - \overline{x})^2$

$\implies \sigma^2 = \frac{6600}{50} = 132$

Hence, Mean = 27 and Variance = 132

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