First slide

Introduction to statistics

Question

The mean of a set of numbers is $\bar{X}$ . If each number is divided by 3, then the new mean is

Easy

A

$\bar{X}$
B

$\bar{X} + 3$
C

$3 \bar{X}$
D

$\frac{\bar{X}}{3}$

Solution

Let $x_{1}, x_{2}, \dots, x_{n}$ n be n numbers. Then $\bar{X} = \frac{1}{n} \sum_{i = 1}^{n} x_{i}$
If each number is divided by 3, then the new mean, $\bar{Y}$ is given by
$\bar{Y} = \frac{1}{n} \sum_{i = 1}^{n} (\frac{x_{i}}{3}) = \frac{1}{3} (\frac{1}{n} \sum_{i = 1}^{n} x_{i}) = \frac{\bar{X}}{3}$

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