Introduction to statistics

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

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Solution

Let $x_{1}, x_{2}, x_{3}, \dots, x_{100}$ be 100 observations. Then
, $\begin{array}{l} Variance = \frac{1}{100} \sum_{i = 1}^{100} x_{i}^{2} - (Mean)^{2} \\ \Rightarrow 25 = \frac{1}{100} \sum_{i = 1}^{100} x_{i}^{2} - 2500 \\ \Rightarrow \sum_{i = 1}^{n} x_{i}^{2} = 252500 \Rightarrow \frac{1}{100} \sum_{i = 1}^{n} x_{i}^{2} = 2525 \end{array}$

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Introduction to statistics

Remember concepts with our Masterclasses.

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

Let x1,x2,x3,…,x100 be 100 observations. Then, Variance =1100∑i=1100 xi2−( Mean )2⇒ 25=1100∑i=1100 xi2−2500⇒ ∑i=1n xi2=252500⇒1100∑i=1n xi2=2525

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