QQuestion
Find the mean of the following frequency distribution using step-deviation method.
Take assumed mean = 28.
| Class interval | Frequency |
|---|---|
| 0–8 | 10 |
| 8–16 | 20 |
| 16–24 | 14 |
| 24–32 | 16 |
| 32–40 | 18 |
| 40–48 | 22 |
Find the mean of the following frequency distribution using step-deviation method.
Take assumed mean = 28.
| Class interval | Frequency |
|---|---|
| 0–8 | 10 |
| 8–16 | 20 |
| 16–24 | 14 |
| 24–32 | 16 |
| 32–40 | 18 |
| 40–48 | 22 |
Here, class size i = 8 and assumed mean A = 28.
| Class interval | f | x | d = x − A | t = d/i | ft |
|---|---|---|---|---|---|
| 0–8 | 10 | 4 | −24 | −3 | −30 |
| 8–16 | 20 | 12 | −16 | −2 | −40 |
| 16–24 | 14 | 20 | −8 | −1 | −14 |
| 24–32 | 16 | 28 | 0 | 0 | 0 |
| 32–40 | 18 | 36 | 8 | 1 | 18 |
| 40–48 | 22 | 44 | 16 | 2 | 44 |
| Total | Σf = 100 | Σft = −22 |
Mean = A + \left(\frac{\sum \mathrm{ft}}{\sum \mathrm{f}}\right)\times \mathrm{i}
= 28 + \left(\frac{-22}{100}\right)\times8
= 28 + 8(-0.22)
= 28 – 1.76
= 26.24
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