Question

Find the value of p, if the mean of the following distribution is 20.

x	15	17	19	20+P	23
f	2	3	4	5P	6

Answer 1

x	f	fx
15	2	30
17	3	51
19	4	76
20+P	5P	100P + 5P2
23	6	138
	N = 5P + 15	`sum`fx = 295 + 100P + 5P2

Given

⇒ Mean = 20

`rArr(sumfx)/N=20`

`rArr(295+100P+5P^2)/(5P+15)=20`

⇒ 295 + 100P + 5P² = 20(5P + 15)

⇒ 295 + 100P + 5P² = 100P + 300

⇒ 100P - 100P + 5P² = 300 - 295

⇒ 5P² = 5

⇒ P² = 1

⇒ P = 1