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Question
Find the mean of the following data using step-deviation method:
| Class | 500 – 520 | 520 – 540 | 540 – 560 | 560 – 580 | 580 – 600 | 600 – 620 |
| Frequency | 14 | 9 | 5 | 4 | 3 | 5 |
Solution
| Class | Frequency `(f_i)` |
Mid values `(x_i)` |
`u_i = ((x_i− A))/ ℎ =( (x_i− 550))/ 20` |
`(f_i × u_i)` |
| 500 – 520 | 14 | 510 | -2 | -28 |
| 520 – 540 | 9 | 530 | -1 | -9 |
| 540 – 560 | 5 | 550=A | 0 | 0 |
| 560 – 580 | 4 | 570 | 1 | 4 |
| 580 – 600 | 3 | 590 | 2 | 6 |
| 600 – 620 | 5 | 610 | 3 | 15 |
| `Ʃ f_i = 40` | `Ʃ (f_i × u_i) = -12` |
Now, A = 550, h = 20, Ʃ` f_i = 40 and Ʃ (f_i × u_i) = -12`
∴ Mean, x =` A + {h xx (Ʃ (f_i × u_i))/(Ʃ f_i)}`
=`550+{20xx ((-12))/40}`
=550-6
=544
∴ x = 544
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