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  • Find the mean and variance for the following frequency distributions. (8)

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

 

Answers (1)

best_answer
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

Posted by

HARSH KANKARIA

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