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NCERT Class XI Mathematics - Statistics - Solutions

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Question : 15 of 34
Marks: +1, -0
First 10 multiples of 3
Solution:  
Here xix_i = 3, 6, 9, 12, 15, 18, 21, 24, 27, 30
∑xi\sum x_i = 3 + 6 + 9 + 12 + 15 + 18 + 21 + 24 + 27 + 30 = 165
n = 10
∴ Mean (x‾)(\overline{x}) = 16510\frac{165}{10} = 16.5
∑xi2\sum x_i^2 =
(3)2+(6)2+(9)2+(12)2(3)^2 + (6)^2 + (9)^2 + (12)^2 + (15)2+(18)2+(21)2+(24)2+(27)2+(30)2(15)^2 + (18)^2 + (21)^2 + (24)^2 + (27)^2 + (30)^2
∴ Variance (σ2)(\sigma^2) = n∑xi2−(∑xi)2n2\frac{n\sum x_i^2 - \left(\sum x_i\right)^2}{n^2}
= 10×3465−(165)2(10)2\frac{10 \times 3465 - (165)^2}{(10)^2} = 34650−27225100\frac{34650 - 27225}{100} = 7425100\frac{7425}{100} = 74.25
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