The mean of the following frequency distribution is $25$. Find the value of $f$.

| Class | $0$-$10$ | $10$-$20$ | $20$-$30$ | $30$-$40$ | $40$-$50$ |
|-------|----------|-----------|-----------|-----

Question

The mean of the following frequency distribution is $25$. Find the value of $f$.

| Class | $0$-$10$ | $10$-$20$ | $20$-$30$ | $30$-$40$ | $40$-$50$ |
|-------|----------|-----------|-----------|-----------|----------|
| Frequency | $5$ | $18$ | $15$ | $f$ | $6$ |

Accepted Answer

Step 1: | Class | $x_i$ | $f$ | $fx$ |
|-------|-------|-----|------|
| $0$-$10$ | $5$ | $5$ | $25$ |
| $10$-$20$ | $15$ | $18$ | $270$ |
| $20$-$30$ | $25$ | $15$ | $375$ |
| $30$-$40$ | $35$ | $f$ | $35f$ |
| $40$-$50$ | $45$ | $6$ | $270$ |
| | | $44 + f$ | $940 + 35f$ |
Step 2: $\bar{x} = 25 = \frac{940 + 35f}{44 + f}$
Step 3: $\Rightarrow f = 16$

Question

Solution