# 5. Find the mean and variance for each of the data. $\small x_i$ 92 93 97 98 102 104 109 $\small f_i$ 3 2 3 2 6 3 3

 $x_i$ $f_i$ $f_ix_i$ $(x_i - \overline{x})$ $(x_i - \overline{x})^2$ $f_i(x_i - \overline{x})^2$ 92 3 276 -8 64 192 93 2 186 -7 49 98 97 3 291 -3 9 27 98 2 196 -2 4 8 102 6 612 2 4 24 104 3 312 4 16 48 109 3 327 9 81 243 $\sum{f_i}$ = 22 $\sum f_ix_i$ = 2200 $\sum f_i(x_i - \overline{x})^2$ =640

$N = \sum_{i=1}^{7}{f_i} = 22 ; \sum_{i=1}^{7}{f_ix_i} = 2200$

$\overline{x} = \frac{1}{N}\sum_{i=1}^{n}f_ix_i = \frac{2200}{22} = 100$

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

$\implies \sigma^2 = \frac{640}{22} = 29.09$

Hence, Mean = 100 and Variance = 29.09

Exams
Articles
Questions