Mathematics
Calculate the mean of the following distribution using step deviation method.
| Marks | No.of students |
|---|---|
| 0 – 10 | 10 |
| 10 – 20 | 9 |
| 20 – 30 | 25 |
| 30 – 40 | 30 |
| 40 – 50 | 16 |
| 50 – 60 | 10 |
Measures of Central Tendency
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Answer
We construct the following table, taking assumed mean a = 25. Here, c (width of each class) = 10.
| Marks | No.of students | Class mark (yi) | ui = (yi - a)/c | No. of students (fi) | fi ui |
|---|---|---|---|---|---|
| 0 – 10 | 10 | 5 | -2 | 10 | -20 |
| 10 – 20 | 9 | 15 | -1 | 9 | -9 |
| 20 – 30 | 25 | a = 25 | 0 | 25 | 0 |
| 30 – 40 | 30 | 35 | 1 | 30 | 30 |
| 40 – 50 | 16 | 45 | 2 | 16 | 32 |
| 50 – 60 | 10 | 55 | 3 | 10 | 30 |
| Total | ∑ fi = 100 | ∑ fi ui = 63 |
By formula,
Hence, mean of the following distribution is 31.3
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