First slide

Introduction to statistics

Question

$If the mean of the numbers 27+x,31+x,89+x,107+x,156+x is 82, then the mean of 130+x, 126+x,68+x,50+x,1+x is$

Easy

A

75
B

157
C

82
D

80

Solution

$Given \begin{array}{l} 82 = \frac{(27 + x) + (31 + x) + (89 + x) + (107 + x) + (156 + x)}{5} \\ \Rightarrow 82 \times 5 = 410 + 5 x \\ \Rightarrow 410 - 410 = 5 x \\ \Rightarrow x = 0 \\ T h e r f o r e, t h e r e q u i r e d m e a n i s \\ \begin{array}{l} \bar{x} = \frac{130 + x + 126 + x + 68 + x + 50 + x + 1 + x}{5} \\ = \frac{375 + 5 x}{5} = \frac{375 + 0}{5} = \frac{375}{5} = 75 \end{array} \end{array}$

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