Question

If the mean of the following data is 20.2, then find the value of p.

xi	10	15	20	25	30
fi	6	8	p	10	6

Answer 1

We have,

${\displaystyle x_i}$	${\displaystyle f_i}$	${\displaystyle x_i{f}_i}$
10	6	60
15	8	120
20	p	20p
25	10	250
30	6	180
	Total N = (30 + p)	Total sum = (610 + 20 p)

since, mean = 20.2

⇒ ${\displaystyle \frac{610+20\text{p}}{30+\text{p}}}$ = 20.2

⇒ 610 + 20p = 20.2 (30 + p)

⇒ 610 + 20p = 606 + 20.2p

⇒ 20.2p - 20p = 610 - 606

⇒ 0.2p = 4

⇒ p = ${\displaystyle \frac{4}{0.2}}$

⇒ p = 20