Mathematics

Calculate the mean of the distribution, given below, using the short cut method :
Marks No. of students
11 - 20 2
21 - 30 6
31 - 40 10
41 - 50 12
51 - 60 9
61 - 70 7
71 - 80 4

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The above distribution is discontinuous, converting into continuous distribution, we get :

Adjustment factor = (Lower limit of one class - Upper limit of previous class) / 2

= $\dfrac{21 - 20}{2} = \dfrac{1}{2}$

= 0.5

Subtract the adjustment factor (0.5) from all the lower limits and add the adjustment factor (0.5) to all the upper limits.

Let assumed mean (A) be 45.5

Marks (Classes before adjustment)	Marks (Classes after adjustment)	Class mean (x)	d = x - A	No. of students (frequency)	fd
11 - 20	10.5 - 20.5	15.5	-30	2	-60
21 - 30	20.5 - 30.5	25.5	-20	6	-120
31 - 40	30.5 - 40.5	35.5	-10	10	-100
41 - 50	40.5 - 50.5	45.5	0	12	0
51 - 60	50.5 - 60.5	55.5	10	9	90
61 - 70	60.5 - 70.5	65.5	20	7	140
71 - 80	70.5 - 80.5	75.5	30	4	120
Total				50	70

n = Σf = 50

Mean = A + $\dfrac{Σfd}{n}$

= $45.5 + \dfrac{70}{50}$

= 45.5 + 1.4

= 46.9

Hence, mean = 46.9

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