Question

Find the vale of p for the following frequency distribution whose mean is 16.6
$\begin{array}{cccccccc}\text{x}& 8& 12& 15& p& 20& 25& 30\\ \text{f}& 12& 16& 20& 24& 16& 8& 4\end{array}$

Answer 1

Sol:

We prepare the following frequency distribution table:

(xi)	(fi)	fixi
8	12	96
12	16	192
15	20	300
p	24	24p
20	16	320
25	8	200
30	4	120
	Σfi=100	Σfixi= 1228+24p

Mean= $\frac{\sum fixi}{\sum xi}$
⇒$16.6=\frac{(1228+24p)}{100}$
⇒$16.6\times 100=1228+24p$
⇒$1660=1228+24p$
⇒$24p=432$

⇒$p=18$