Calculate the mean and standard deviation for the following table given the age distribution of a group of people: Age: 20-30 30-40 40-50 50-60 60-70 70-80 80-90 No. of persons: 3 51 122 141 130 51 2

Explanation

`sum f_{i} u_{i}=25`

`f_{i} u_{i}^{2}=705`

`N=sum f_{i}=500 therefore` Variance `(sigma^{2})=[frac{sum f_{i} u_{i}^{2}}{N}-(frac{sum f_{i} u_{i}}{N})^{2}] h^{2}`

`h=` Class size `=10`

`therefore sigma^{2}=[frac{705}{500}-(frac{25}{500})^{2}] cdot 10^{2}=10^{2}(1.4075)`

`therefore` Standard deviation `(sigma)=sqrt{10^{2}(1.4075)}=10 * 1.186=11.86`

Mean `(bar{X})=A+h[frac{sum f_{i} u_{i}}{N}]`

Here, `A=` Assumed Mean `=55`

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