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Question
Find the mean and variance of the frequency distribution given below:
| `x` | 1 ≤ x < 3 | 3 ≤ x < 5 | 5 ≤ x < 7 | 7 ≤ x < 10 |
| `f` | 6 | 4 | 5 | 1 |
Solution
| `x` | `f_i` | `x_i` | `f_ix_i` | `f_ix_i^2` |
| 1 – 3 | 6 | 2 | 12 | 24 |
| 3 – 5 | 4 | 4 | 16 | 64 |
| 5 – 7 | 5 | 6 | 30 | 180 |
| 7 – 10 | 1 | 8.5 | 8.5 | 72.25 |
| N = 16 | `sumf_ix_i` = 66.5 | `sumf_ix_i^2` = 340.25 |
Mean = `(sumf_ix_i)/N = 66.5/6` = 4.15
Varaince `(sigma^2) = (sumf_ix_i^2)/N - ((sumfx)/N)^2`
= `340.25/16 - (4.15)^2`
= 21.26 – 17.22
= 4.04
Hence, the required mean = 4.15 and variance = 4.04
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