Question

The mean of the following distribution is 6. Find the value at P:

x	2	4	6	10	P + 5
f	3	2	3	1	2

Answer 1

Calculation of Arithmetic Mean:

`x_i`	`f_i`	`f_ix_i`
2	3	6
4	2	8
6	3	18
10	1	10
P + 5	2	2P + 10
	`sumf_i` = 11	`sumf_ix_i` = 2P + 52

We have,
`sumf_i` = 11
`sumf_ix_i` = 2P + 52
∴ Mean = `(sumf_ix_i)/(sumf_i)`
6 = `(2P + 52)/(11)`
⇒ 66 = 2P + 52
⇒  2P = 66 - 52
⇒  2P = 14
⇒  P = 7.