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UPSC NDA 2 2021 Mathematics Solved Paper

Question : 116 of 120

Marks: +1, -0

\displaystyle \sum_{i=1}^{10} x_i = 110

\displaystyle \sum_{i=1}^{10} x_i^2 = 1540

then what is the variance?

Solution:

Concept:

Variance measures the average squared deviation of data points from their mean.

Explanation:

Given

n = 10

\sum x_i = 110

, and

\sum x_i^2 = 1540

First, find the mean:

\bar{x} = \frac{\sum x_i}{n} = \frac{110}{10} = 11

Variance formula:

V = \frac{\sum x_i^2}{n} - (\bar{x})^2

Substitute values:

V = \frac{1540}{10} - (11)^2 = 154 - 121 = 33

Thus, the variance is 33.

Answer:

B. 33

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