Question

The mean of the following frequency data is 42, Find the missing frequencies x and y if the sum of frequencies is 100.

Class interval	0 – 10	10 – 20	20 – 30	30 – 40	40 – 50	50 – 60	60 – 70	70 – 80
Frequency	7	10	x	13	y	10	14	9

Find x and y.

Answer 1

The given data is shown as follows:

Class Interval	Frequency (fi)	Class mark (xi)	fixi
0 – 10	7	5	35
10 – 20	10	15	150
20 – 30	x	25	25x
30 – 40	13	35	455
40 – 50	y	45	45y
50 – 60	10	55	550
60 – 70	14	65	910
70 – 80	9	75	675
Total	Σfi = 63 + x + y		Σfixi = 2775 + 25x + 45y

Sum of the frequencies = 100

⇒ Σ_if_i = 100
⇒ 63 + x + y = 100
⇒ x + y = 100 – 63
⇒ x + y = 37
⇒ y = 37 – x           ……..(1)
Now, the mean of the given data is given by

`barx = (sumf_ix_i)/(sumf_i )`

⇒ 42 =`(2775+25x+45y)/100`
⇒ 4200 = 2775 + 25x + 45y
⇒ 4200 – 2775 = 25x + 45y
⇒ 1425 = 25x + 45(37 – x)          [from (1)]
⇒ 1425 = 25x + 1665 – 45x
⇒ 20x = 1665 – 1425
⇒ 20x = 240
⇒ x = 12
If x = 12, then y = 37 – 12 = 25
Thus, the value of x is 12 and y is 25.