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प्रश्न
Find the Arithmetic Mean of the following data using Step Deviation Method:
| Age | 15 − 19 | 20 − 24 | 25 − 29 | 30 − 34 | 35 − 39 | 40 − 44 |
| No. of persons | 4 | 20 | 38 | 24 | 10 | 9 |
योग
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उत्तर
Assumed Mean (A) = 32
| Age | Mid value (x) |
Frequency (f) |
d = `(x - "A")/4` | fd |
| 15 − 19 | 17 | 4 | = `(17 - 32)/4` = −3.75 | −15 |
| 20 − 24 | 22 | 20 | = `(22 - 32)/4` = −2.5 | −50 |
| 25 − 29 | 27 | 38 | = `(27 - 32)/4` = −1.25 | −47.5 |
| 30 − 34 | 32 | 24 | = `(32 - 32)/4` = 0 | 0 |
| 35 − 39 | 37 | 10 | = `(37 - 32)/4` = 1.25 |
12.5 |
| 40 − 44 | 42 | 9 | = `(42 - 32)/4` = 2.5 | 22.5 |
| `sumf` = 105 | `sumf"d"` = −77.5 |
Arithmetic mean = `"A" + (sumf"d")/(sumf) xx "c"`
= `32 + ((-77.5)/105 xx 4)`
= 32 – 2.95
= 29.05
Arithmetic mean = 29.05
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