Mathematics

The mean of the following distribution is 52 and the frequency of class-interval 30 - 40 is 'f'. Find 'f'.
Class Interval Frequency
10 - 20 5
20 - 30 3
30 - 40 f
40 - 50 7
50 - 60 2
60 - 70 6
70 - 80 13

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Class Interval	Class mean (x)	Frequency (f)	fx
10 - 20	15	5	75
20 - 30	25	3	75
30 - 40	35	f	35f
40 - 50	45	7	315
50 - 60	55	2	110
60 - 70	65	6	390
70 - 80	75	13	975
Total		Σf = 36 + f	1940 + 35f

By formula,

⇒ Mean = $\dfrac{Σfx}{Σf}$

⇒ 52 = $\dfrac{1940 + 35f}{36 + f}$

⇒ 52(36 + f) = 1940 + 35f

⇒ 1872 + 52f = 1940 + 35f

⇒ 52f - 35f = 1940 - 1872

⇒ 17f = 68

⇒ f = $\dfrac{68}{17}$ = 4.

Hence, f = 4.

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