Find the mean and variance for the following frequency distribution.

 Classes 0-10 10-20 20-30 30-40 40-50 Frequencies 5 8 15 16 6

Asked by Abhisek | 11 months ago |  82

##### Solution :-

$$Mean,\overline{x}= A +\dfrac{\displaystyle\sum_{i=1}{f_i}u_i }{N}× h$$

$$25 +\dfrac{10}{50}× 10$$

= 25 + 2 = 27

Now, Variance,

$$σ^2= \dfrac{h^2}{N^2}[N\displaystyle\sum_{i=1}{f_i}u_i^2-(\displaystyle\sum_{i=1}{f_i}u_i)^2]$$

$$\dfrac{(10)^2}{(50)^2}[50\times 68-(10)^2]$$

$$\dfrac{1}{25^2}[3400 =1000]$$

$$\dfrac{3300}{25}$$

= 132

Answered by Abhisek | 11 months ago

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