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NCERT Class XI Mathematics - Statistics - Solutions

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Question : 13 of 34
Marks: +1, -0
6, 7, 10, 12, 13, 4, 8, 12
Solution:  
Here xi = 6, 7, 10, 12, 13, 4, 8, 12
∴ Σ xix_i = 6 + 7 + 10 + 12 + 13 + 4 + 8 + 12 = 72; n = 8
∴ Mean (x)(\overline{x}) = 728\frac{72}{8} = 9
Now, Sx2i= (6)2+(7)2+(10)2+(12)2(6)^2 + (7)^2 + (10)^2 + (12)^2 + (13)2+(4)2+(8)2+(12)2(13)^2 + (4)^2 + (8)^2 + (12)^2
= 36 + 49 + 100 + 144 + 169 + 16 + 64 + 144 = 722
∴ Variance (σ2)(\sigma^2) = nΣxi2(Σxi)2n2\frac{n\Sigma x_i^2 - (\Sigma x_i)^2}{n^2} = 8×722(72)2(8)2\frac{8\times 722 - (72)^2}{(8)^2}
= 5776518464\frac{5776 - 5184}{64} = 59264\frac{592}{64} = 9.25
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