| $x:$ | $5$ | $8$ | $10$ | $12$ | $p$ | $20$ | $25$ |
| $f:$ | $2$ | $5$ | $8$ | $22$ | $7$ | $4$ | $2$ |
Solution:
| $x$ | $f$ | $fx$ |
| $5$ | $2$ | $10$ |
| $8$ | $5$ | $40$ |
| $10$ | $8$ | $80$ |
| $12$ | $22$ | $264$ |
| $P$ | $7$ | $7p$ |
| $20$ | $4$ | $80$ |
| $25$ | $2$ | $50$ |
| $N=50$ | $\sum{fx=524+7p}$ |
We know that,
Mean $=\sum{fx/N=\left( 524+7P \right)}/50$
Given,
Mean $=12.58$
$\Rightarrow 12.58=\left( 524+7P \right)/50$
$629=524+7p$
$7p=629-524=105$
$\therefore p=15$