First slide

Introduction to statistics

Question

If the mean of a set of observations $x_{1}, x_{2},$
$\dots, x_{10}$ is $20$ then the mean of $x_{1} + 4, x_{2} + 8, x_{3} + 12, \dots, x_{10}$
$+ 40$ is

Easy

A

34
B

42
C

38
D

40

Solution

Required mean $= \frac{1}{10} [[(x_{1} + x_{2} + \dots x_{10}) +$
$(4 + 8 + \dots 40)$
$\begin{array}{l} = \frac{1}{10} (x_{1} + \dots + x_{10}) + \frac{4}{10} [1 + 2 + \dots + 10] \\ = 20 + \frac{4 \times 10 \times 11}{10 \times 2} = 42 . \end{array}$

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