First slide

Introduction to statistics

Question

The mean of 100 observations is 50 and their standard deviation is 5. The sum of squares of all the observations is

Easy

A

50000
B

250000
C

252500
D

255000

Solution

$\begin{array}{l} Given, \bar{x} = 50, n = 100 and σ = 5 \\ \Rightarrow 50 = \frac{Σ x_{i}}{100} \\ \Rightarrow Σ x_{i} = 50 \times 100 = 5000 \\ Now, σ^{2} = \frac{Σ x_{i}^{2}}{n} - (\bar{x})^{2} \\ \Rightarrow 25 = \frac{Σ x_{i}^{2}}{100} - (50)^{2} \\ \Rightarrow 2525 = \frac{Σ x_{i}^{2}}{100} \\ ∴ Σ x_{i}^{2} = 252500 \end{array}$

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