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Find the mean and variance for each of the data. (4)

4. Find the mean and variance for each of the data.

\small x_i 6 10 14 18 24 28 30
\small f_i 2 4 7 12 8 4 3

 

Answers (1)
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x_i f_i f_ix_i (x_i - \overline{x}) (x_i - \overline{x})^2 f_i(x_i - \overline{x})^2
2 12 -13 169 338
10 4 40 -9 81 324
14 7 98 -5 25 175
18 12 216 -1 1 12
24 8 192 5 25 200
28 4 112 9 81 324
30 3 90 13 169 363
 

\sum{f_i}

= 40

\sum f_ix_i

= 760

   

\sum f_i(x_i - \overline{x})^2

=1736

N = \sum_{i=1}^{7}{f_i} = 40 ; \sum_{i=1}^{7}{f_ix_i} = 760

\overline{x} = \frac{1}{N}\sum_{i=1}^{n}f_ix_i = \frac{760}{40} = 19

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

\implies \sigma^2 = \frac{1736}{40} = 43.4

Hence, Mean = 19 and Variance = 43.4

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