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Question
Find the mean of the following data, using assumed-mean method:
| Class | 0 – 20 | 20 – 40 | 40 – 60 | 60 – 80 | 80 – 100 | 100 - 120 |
| Frequency | 20 | 35 | 52 | 44 | 38 | 31 |
Solution
| Class | Frequency `(f_i)` | Mid values `(x_i)` | Deviation `(d_i) d_i = (x_i – 50)` |
`(f_i × d_i)` |
| 0 –20 | 20 | 10 | -40 | -800 |
| 20 –40 | 35 | 30 | -20 | -700 |
| 40 –60 | 52 | 50=A | 0 | 0 |
| 60 – 80 | 44 | 70 | 20 | 880 |
| 80 – 100 | 38 | 90 | 40 | 1520 |
| 100 – 120 | 31 | 110 | 60 | 1860 |
| `Ʃ f_i `= 220 | `Ʃ (f_i × d_i) `= 2760 |
Let A = 50 be the assumed mean. Then we have:
Mean, x = A +`(Ʃ (f_i × d_i))/( Ʃ f_i)`
=50+`2760/220`
= 50+ 12.55
∴ x = 62.55
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