First slide

Introduction to statistics

Question

The mean of the series $x_{1}, x_{2}, \dots, x_{n} is \bar{X} . If x_{2}$ is replaced by $λ,$ then the new mean is

Moderate

A

$\bar{X} - x_{2} + λ$
B

$\frac{\bar{X} - x_{2} - λ}{n}$
C

$\frac{(n - 1) \bar{X} + λ}{n}$
D

$\frac{n X - x_{2} + λ}{n}$

Solution

We have,
$\begin{array}{l} \bar{X} = \frac{x_{1} + x_{2} + \dots + x_{n - 1} + x_{n}}{n} \\ \Rightarrow n \bar{X} = x_{1} + x_{2} + \dots + x_{n - 1} + x_{n} \end{array}$
$n e w m e a n = \frac{n X - x_{2} + λ}{n}$

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