Question

The arithmetic mean of the following data is 14. Find the value of k

x1	5	10	15	20	25
f1	7	k	8	4	5

Answer 1

x1	f1	x1f1
5	7	35
10	k	10k
15	8	120
20	4	80
25	5	125
	`sumf_1=24+k`	`sumx_1f_1=360+10k`

We know that mean, `barx=(sumx_1f_1)/(sumf_1)`

`14=(360+10k)/(24+k)`

By using cross multiplication method,

14(24 + k) = 360 + 10k

336 + 14k = 360 + 10k

14k - 10k = 360 - 336

4k = 24

`k=24/4`

Hence, k = 6