Question

The arithmetic mean of the following data is 25, find the value of k.

x1	5	15	25	35	45
f1	3	k	3	6	2

Answer 1

x	f	fx
5	3	15
15	k	15k
25	3	75
35	6	210
45	2	90
	N = k + 14	`sum`fx = 15k + 390

Given

Mean = 25

`rArr(sumfx)/N=25`

`rArr(15k+390)/(k+14)=25`

⇒ 15k + 390 = 25(k + 14)

⇒ 15k + 390 = 25k + 350

⇒ 25k - 15k = 390 - 350

⇒ 10k = 40

`rArr k=40/10`

⇒ k = 4