Question

The arithmetic mean of the following frequency distribution is 53. Find the value of k.

Class	0-20	20-40	40-60	60-80	80-100
Frequency	12	15	32	k	13

Answer 1

Class	Frequency (fi)	xi	di = xi -50	fidi
0 - 20	12	10	-40	-480
20 - 40	15	30	-20	-300
40 - 60	32	50	0	0
60 - 80	k	70	20	20k
80 - 100	13	90	40	520
	∑fi = 72 + k			fidi = -260 + 20k

`bar"x" = "a" + (∑"f"_"i" "d"_"i")/(∑"f"_"i")`

`53 = 50 + ((-260 + 20"k"))/(72 +" k")`

⇒ 3 = `(-260 + 20"k")/(72 +"k")`

⇒ `216 + 3"k" = -260 + 20"k"`
⇒  `476 = 17"k"`
⇒ k = 28