Question

If the mean of the following frequency distribution is 54, find the value of p.
$\begin{array}{cccccc}\text{Class}& 0-20& 20-40& 40-60& 60-80& 80-100\\ \text{Frequency}& 7& p& 10& 9& 13\end{array}$

Answer 1

The given data is shown as follows:

Class	Frequency (fi)	Class mark (xi)	(fixi)
0 - 20	7	10	70
20 - 40	p	30	30p
40 - 60	10	50	500
60 - 80	9	70	630
80 - 100	13	90	1170
Total	∑fi=39+p		∑(fi×xi)=2370+30p

The mean of given data is given by

$\overline{x}$= ∑(fi×xi)/∑fi

⇒ 54 = $\frac{2370+30p}{39+p}$
⇒ 54(39 + p) = 2370 + 30p

⇒ 2106 + 54p = 2370 + 30p

⇒ 54p - 30p = 2370-2106

⇒ 24p = 264

⇒ p = 11

Hence, the value of p is 11.