Find the mean of the following data using assumed mean method:

| Class | $0$-$5$ | $5$-$10$ | $10$-$15$ | $15$-$20$ | $20$-$25$ |
|-------|---------|----------|-----------|-----------|----------|
| F

Question

Find the mean of the following data using assumed mean method:

| Class | $0$-$5$ | $5$-$10$ | $10$-$15$ | $15$-$20$ | $20$-$25$ |
|-------|---------|----------|-----------|-----------|----------|
| Frequency | $8$ | $7$ | $10$ | $13$ | $12$ |

Accepted Answer

Step 1: Using assumed mean $a = 12.5$:

| Class | $x_i$ | $f$ | $d = x_i - 12.5$ | $fd$ |
|-------|-------|-----|-------------------|------|
| $0$-$5$ | $2.5$ | $8$ | $-10$ | $-80$ |
| $5$-$10$ | $7.5$ | $7$ | $-5$ | $-35$ |
| $10$-$15$ | $12.5$ | $10$ | $0$ | $0$ |
| $15$-$20$ | $17.5$ | $13$ | $5$ | $65$ |
| $20$-$25$ | $22.5$ | $12$ | $10$ | $120$ |
| | | $50$ | | $70$ |
Step 2: $\bar{x} = 12.5 + \frac{70}{50} = 12.5 + 1.4 = 13.9$

Question

Solution