Question

If the median of the following frequency distribution is 32.5. Find the values of f₁ and f_2.

Answer 1

Class	Frequency	Cumulative Frequency
0-10	f1	f1
10-20	5	5 + f1
20-30	9	14+f1
30-40	12	26+f1
40-50	f2	26+f1+f2
50-60	3	29+f1+f2
60-70	2	31+f1 + f2
Total		40 n

F₁ + 5 + 9 + 12 + f₂ + 3 + 2 = 40

f₁ + f₂ = 40 - 31 = 9 ...(i)

Medians= 32.5 Given

Since, Median class is 30-40

l = 30, h = 10, cf = 14 + f₁,f = 12

Median = l + `(("n"/2 - "cf")/"f") xx "h"`

32.5 = 30 `[(40/2 - (14 + f2))/12] xx 10`

2.5 = `10/(12(20 -14-f_1)`

3=6 - f₁

f₂ = 3 

On putting in (i)

f1 + f2 = 9

f₂ = 9-3  [∵ f₁ = 3]

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