Find the arithmetic mean of the following data by shortcut method.

Class Interval	0 – 10	10 – 20	20 – 30	30 – 40	40 – 50	50 – 60
Frequency	4	8	13	20	12	8

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answer is D.

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Detailed Solution

We have to find the mean using the shortcut method.
The mean

\underset{̲}{x}

is given by the formula,

\underset{̲}{x}

\frac{\sum X_{i} f_{i}}{\sum f_{i}}

We have our data as,

Class Interval	Frequency
0 – 10	4
10 – 20	8
20 – 30	13
30 – 40	20
40 – 50	12
50 – 60	8

Let us assume A = 13, then we will calculate di = xi −A, i = 1, 2, …6 and fidi . But before doing so, we need xi , i=1,2,.....6 as here class interval is given as xi = mid point of class interval.
This gives our new table as

Class Interval	xi	fi	di =xi − A	fidi
0 – 10	5	4	– 20	– 80
10 – 20	15	8	– 10	– 80
20 – 30	25 = A	13	0	0
30 – 40	35	20	10	200
40 – 50	45	12	20	240
50 – 60	55	8	30	240
		N = 65		520