| $x:$ | $8$ | $12$ | $15$ | $p$ | $20$ | $25$ | $30$ |
| $f:$ | $12$ | $16$ | $20$ | 24 | $16$ | $8$ | $4$ |
Solution:
| $x$ | $f$ | $fx$ |
| $8$ | $12$ | $96$ |
| $12$ | $16$ | $192$ |
| $15$ | $20$ | $300$ |
| $P$ | $24$ | $24p$ |
| $20$ | $16$ | $320$ |
| $25$ | $8$ | $200$ |
| $30$ | $4$ | $120$ |
| $N=100$ | $\sum{fx=1228+24p}$ |
We know that,
Mean $=\sum{fx/N=\left( 1228+24p \right)}/100$
Given,
Mean $=16.6$
$\Rightarrow 16.6=\left( 1228+24p \right)/100$
$1660=1228+24p$
$25p=432$
$\therefore p=18$