First slide

Introduction to statistics

Question

$If the mean of the numbers 27 + x, 31 + x, 89 + x, 107 + x, 156 + x i s 82, t h e n t h e m e a n o f 130 + x, 126 + x, 68 + x, 50 + x, 1 + x i s$

Easy

A

75
B

157
C

82
D

80

Solution

Given
$\begin{aligned} 82 = \frac{(27 + x) + (31 + x) + (89 + x) + (107 + x) + (156 + x)}{5} \\ \Rightarrow 82 \times 5 = 410 + 5 x \Rightarrow 410 - 410 = 5 x \Rightarrow x = 0 \end{aligned}$
Therefore, the required mean is
$\begin{aligned} \bar{x} = \frac{130 + x + 126 + x + 68 + x + 50 + x + 1 + x}{5} \\ = \frac{375 + 5 x}{5} = \frac{375 + 0}{5} = \frac{375}{5} = 75 \end{aligned}$

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