First slide

Introduction to statistics

Question

${Let x}_{1}, x_{2}, \dots, x_{n} be \sum_{i = 1}^{n} x_{i}^{2} = 400 and \sum_{i = 1}^{n} x_{i} = 80 . Then a possible value of n among the following is$

Moderate

A

9
B

12
C

15
D

18

Solution

$Since square root of mean of square ≥ arithmetic mean$
$\sqrt{\frac{\sum_{i = 1}^{n} x_{i}^{2}}{n}} \geq \frac{\sum_{i = 1}^{n} x_{i}}{n} = \sqrt{\frac{400}{n}} \geq \frac{80}{n} \Rightarrow n \geq 16$
$H e n c e, t h e p o s s i b l e v a l u e s o f n i s 18$ from the options

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