Mathematics
Find mean by 'step-deviation method' :
| C.I. | Frequency |
|---|---|
| 63 - 70 | 9 |
| 70 - 77 | 13 |
| 77 - 84 | 27 |
| 84 - 91 | 38 |
| 91 - 98 | 32 |
| 98 - 105 | 16 |
| 105 - 112 | 15 |
Measures of Central Tendency
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Answer
Let assumed mean (A) be 87.5 and i = 7.
| C.I. | Class mark (x) | Frequency (f) | d = x - A | t = (x - a)/i | ft |
|---|---|---|---|---|---|
| 63 - 70 | 66.5 | 9 | 66.5 - 87.5 = -21 | -3 | -27 |
| 70 - 77 | 73.5 | 13 | 73.5 - 87.5 = -14 | -2 | -26 |
| 77 - 84 | 80.5 | 27 | 80.5 - 87.5 = -7 | -1 | -27 |
| 84 - 91 | 87.5 | 38 | 87.5 - 87.5 = 0 | 0 | 0 |
| 91 - 98 | 94.5 | 32 | 94.5 - 87.5 = 7 | 1 | 32 |
| 98 - 105 | 101.5 | 16 | 101.5 - 87.5 = 14 | 2 | 32 |
| 105 - 112 | 108.5 | 15 | 108.5 - 87.5 = 21 | 3 | 45 |
| Total | Σf = 160 | Σft = 29 |
n = Σf = 160.
By formula,
Mean = A +
= 87.5 +
= 87.5 +
= 87.5 + 1.3
= 88.8
Hence, mean = 88.8
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