First slide

Introduction to statistics

Question

$Let x_{1}, x_{2}, \dots \dots x_{n} be n observations such that \sum_{i = 1}^{n} x_{i}^{2} = 300 and \sum_{i = 1}^{n} x_{i} = 60 . Then a possible$ $value of n among the following is.$

Moderate

A

5
B

10
C

15
D

11

Solution

$Given that \sum x_{i}^{2} = 300 and \sum x_{i} = 60$
$\begin{array}{l} \frac{\sum_{i = 1}^{n} x_{i}^{2}}{n} \geq {(\frac{\sum_{i = 1}^{n} x_{i}}{n})}^{2} \\ \Rightarrow \frac{300}{n} \geq {(\frac{60}{n})}^{2} \\ n \geq 12 \\ ∴ By options, the possible value of n is 15 \end{array}$

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