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  • Find the mean and variance for each of the data (5)

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

 

Answers (1)

best_answer
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

Posted by

HARSH KANKARIA

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