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Question
Find the mean and variance for the data.
| xi | 92 | 93 | 97 | 98 | 102 | 104 | 109 |
| fi | 3 | 2 | 3 | 2 | 6 | 3 | 3 |
Solution
Let the assumed mean A = 98,
∴ yi = xi – 98
| xi | fi | yi | fyi | `y_i^2` | `fy_i^2` |
| 92 | 3 | −6 | −18 | 36 | 108 |
| 93 | 2 | −5 | −10 | 25 | 50 |
| 97 | 3 | −1 | −3 | 1 | 3 |
| 98 | 2 | 0 | 0 | 0 | 0 |
| 102 | 6 | 4 | 24 | 16 | 96 |
| 104 | 3 | 6 | 18 | 36 | 108 |
| 109 | 3 | 11 | 33 | 121 | 363 |
| Sum | 22 | - | 44 | - | 728 |
Mean = `A + (sumf_iy_i)/N`
= `98 + 44/22`
= 98 + 2
= 100
Variance `σ^2 = 1/N^2 [N sum f_iy_i - (sumf_iy_i)^2]`
= `1/(22)^2 [22 xx 728 - 44 xx 44]`
= `1/22[728 - 88]`
= `640/22`
= `320/11`
= 29.09
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