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Question
Find the arithmetic mean of the following frequency distribution using step-deviation method:
| Age (in years) | 18 – 24 | 24 – 30 | 30 – 36 | 36 – 42 | 42 – 48 | 48 – 54 |
| Number of workers | 6 | 8 | 12 | 8 | 4 | 2 |
Solution
| Class | Frequency `(f_i)` | Mid values `(x_i)` | `u_i =( (x_i− A))/ ℎ = ((x_i− 33))/ 6` |
`(f_i× u_i)` |
| 18 – 24 | 6 | 21 | -2 | -12 |
| 24 – 30 | 8 | 27 | -1 | -8 |
| 30 – 36 | 12 | 33 = A | 0 | 0 |
| 36 – 42 | 8 | 39 | 1 | 8 |
| 42 – 48 | 4 | 45 | 2 | 8 |
| 48 – 54 | 2 | 51 | 3 | 6 |
| Total | `Ʃ f_i = 40` | `Ʃ (f_i × u_i) = 2` |
Now, A = 33, h = 6, `Ʃ f_i = 40 and Ʃ (f_i × u_i) = 2`
∴ Mean, x = A + `{ h xx (Ʃ (f_i × u_i))/(Ʃ f_i)}`
=`33+ { 6xx2/40}`
= 33 + 0.3
= 33.3
∴ x = 33.3 years
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