Q.
The mean of the given data is $30$.
Class
$0-10$
$10-20$
$20-30$
$30-40$
$40-50$
Frequency
$8$
$10$
$f_1$
$15$
$f_2$
If total data is $70$, then missing numbers are
| Class | $0-10$ | $10-20$ | $20-30$ | $30-40$ | $40-50$ |
| Frequency | $8$ | $10$ | $f_1$ | $15$ | $f_2$ |
Statistics
Solution:
We have,
Class
$x$
$f$
$fx$
$0-10$
$5$
$8$
$40$
$10-20$
$15$
$10$
$150$
$20-30$
$25$
$f_1$
$25\,f_1$
$30-40$
$35$
$15$
$525$
$40-50$
$45$
$f_2$
$45\,f_2$
Also, $\Sigma f = 70$, $\Sigma f x = 25f_{1}+45f_{2}+715$
$\Rightarrow 8 + 10 + f_{1}+ 15 + f_{2} = 70$
$\Rightarrow f_{1}+f_{2} = 37\quad\ldots\left(i\right)$
and $\bar{x} = \frac{\Sigma fx}{\Sigma f}$
$\Rightarrow 5f_{1}+9f_{2} = 277\quad\ldots\left(ii\right)$
Solving $\left(i\right)$ and $\left(ii\right)$, we get $f_{1} = 14$ and $f_{2} = 23$
| Class | $x$ | $f$ | $fx$ |
|---|---|---|---|
| $0-10$ | $5$ | $8$ | $40$ |
| $10-20$ | $15$ | $10$ | $150$ |
| $20-30$ | $25$ | $f_1$ | $25\,f_1$ |
| $30-40$ | $35$ | $15$ | $525$ |
| $40-50$ | $45$ | $f_2$ | $45\,f_2$ |