__Methods of calculating mean of grouped frequency distribution :__

__Direct Method :__Let x

_{i}be class mark and f

_{i}be frequency of i

^{th}class interval. Mean = (Total f

_{i}x

_{i}) / (Total f

_{i})

__Assumed Mean Method :__Let x

_{i}be class mark of i

^{th}class interval, A be assumed mean and d

_{i}be x

_{i}- A.

Mean of d

_{i}= (Total f_{i}d_{i}) / (Total f_{i})
Total mean = A + mean of d

_{i}.__Step Deviation Method :__Let d

_{i}= x

_{i}- A, u

_{i}= d

_{i }/ h where h is class width.

Mean of u

_{i}= (Total f_{i}u_{i}) / (Total f_{i})
Total mean = A + (mean of u

_{i})h.__Method of calculating median of grouped frequency distribution :__

- Write given class intervals in column 1, respective frequencies in column 2, cumulative frequency less than type in column 3.
- Find total frequency N = Total f
_{i}, find N/2, and then find c.f. less than type which is > or = N/2. That class is median class. - find median using formula Median = L(N/2 - c.f.).h/f where L is lower limit and h is width of median class.

__Method of calculating mode of grouped frequency distribution :__

- Find maximum frequency (f
_{m}), determine its class called the modal class. - Find mode using formula Mode = L + [ (f
_{m}-f_{1}) / (f_{m}- f_{1}- f_{2}) ]h where L is lower limit of modal class, f_{1}is premodal frequency and f_{2}is postmodal frequency.

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