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TS EAMCET · Maths · Statistics

The mean and standard deviation of 100 observations \(x_1, x_2, \ldots, x_{100}\) were calculated as 40 and 5.1 respectively by a student who took by mistake 50 instead of 40 for one observation. Then the correct value of \(\sum_{i=1}^{100} x_i^2=\)

  1. A 3990
  2. B 161701
  3. C 162601
  4. D 4000
Verified Solution

Answer & Solution

Correct Answer

(B) 161701

Step-by-step Solution

Detailed explanation

\(\begin{aligned} & \text { Given, } x=40, \sigma=5 \cdot 1, n=100 \\ & \qquad \sigma^2=\frac{\Sigma x_i^2}{100}-(\bar{x})^2 \Rightarrow(5 \cdot 1)^2=\frac{\Sigma x_1^2}{100}-(40)^2\end{aligned}\) \(\Sigma x_1^2=(26.01+1600) \times 100=2601+1600 \times 100\) The correct value of…