Find the mean of the following frequency distribution:

| Classes | $25 - 30$ | $30 - 35$ | $35 - 40$ | $40 - 45$ | $45 - 50$ | $50 - 55$ | $55 - 60$ |
|---------|-----------|-----------|-----------|-

Question

Find the mean of the following frequency distribution:

| Classes | $25 - 30$ | $30 - 35$ | $35 - 40$ | $40 - 45$ | $45 - 50$ | $50 - 55$ | $55 - 60$ |
|---------|-----------|-----------|-----------|-----------|-----------|-----------|----------|
| Frequency | $14$ | $22$ | $16$ | $6$ | $5$ | $3$ | $4$ |

Accepted Answer

Step 1: Using assumed mean method with $a = 42.5$, $h = 5$:

| C.I. | $x$ | $f$ | $u = \frac{x - 42.5}{5}$ | $fu$ |
|------|------|-----|------|------|
| $25 - 30$ | $27.5$ | $14$ | $-3$ | $-42$ |
| $30 - 35$ | $32.5$ | $22$ | $-2$ | $-44$ |
| $35 - 40$ | $37.5$ | $16$ | $-1$ | $-16$ |
| $40 - 45$ | $42.5$ | $6$ | $0$ | $0$ |
| $45 - 50$ | $47.5$ | $5$ | $1$ | $5$ |
| $50 - 55$ | $52.5$ | $3$ | $2$ | $6$ |
| $55 - 60$ | $57.5$ | $4$ | $3$ | $12$ |
| **Total** | | $70$ | | $-79$ |
Step 2: Mean $= a + \frac{\sum fu}{\sum f} 	imes h = 42.5 - \frac{79}{70} 	imes 5 = 42.5 - 5.64 = 36.86$

Question

Solution