Find the Mean and Mode of the following frequency distribution:

| Class | Frequency |
|-------|-----------|
| $0 - 10$ | $8$ |
| $10 - 20$ | $7$ |
| $20 - 30$ | $15$ |
| $30 - 40$ | $20$ |
| $40 - 50

Question

Find the Mean and Mode of the following frequency distribution:

| Class | Frequency |
|-------|-----------|
| $0 - 10$ | $8$ |
| $10 - 20$ | $7$ |
| $20 - 30$ | $15$ |
| $30 - 40$ | $20$ |
| $40 - 50$ | $12$ |
| $50 - 60$ | $8$ |
| $60 - 70$ | $10$ |

Accepted Answer

Step 1: Using step-deviation method with assumed mean $a = 35$, $h = 10$:

| Class | $f_i$ | $x_i$ | $u_i = \frac{x_i - 35}{10}$ | $f_i u_i$ |
|-------|--------|--------|------|----------|
| $0 - 10$ | $8$ | $5$ | $-3$ | $-24$ |
| $10 - 20$ | $7$ | $15$ | $-2$ | $-14$ |
| $20 - 30$ | $15$ | $25$ | $-1$ | $-15$ |
| $30 - 40$ | $20$ | $35$ | $0$ | $0$ |
| $40 - 50$ | $12$ | $45$ | $1$ | $12$ |
| $50 - 60$ | $8$ | $55$ | $2$ | $16$ |
| $60 - 70$ | $10$ | $65$ | $3$ | $30$ |
| Total | $80$ | | | $5$ |
Step 2: Mean $= 35 + \frac{5}{80} 	imes 10 = 35 + 0.625 = 35.625$
Step 3: Modal class is $30 - 40$ (highest frequency $= 20$).
Mode $= 30 + \left(\frac{20 - 15}{2 	imes 20 - 15 - 12}ight) 	imes 10$
Step 4: $= 30 + \frac{5}{13} 	imes 10 = 30 + \frac{50}{13} \approx 33.85$ approx.

Question

Solution