7.Find the mean and variance for the following frequency distributions.

Classes 0-30 30-60 60-90 90-120 120-150 150-180 180-210
Frequencies 2 3 5 10 3 5 2

 

Answers (1)
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
0-30 2 15 30 -92 8464 16928
30-60 3 45 135 -62 3844 11532
60-90 5 75 375 -32 1024 5120
90-120 10 105 1050 2 4 40
120-150 3 135 405 28 784 2352
150-180 5 165 825 58 3364 16820
180-210 2 195 390 88 7744 15488
 

\sum{f_i} = N

= 30

 

\sum f_ix_i

= 3210

   

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

=68280

 

\overline{x} = \frac{1}{N}\sum_{i=1}^{n}f_ix_i = \frac{3210}{30} = 107

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

\implies \sigma^2 = \frac{68280}{30} = 2276

Hence, Mean = 107 and Variance = 2276

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