First slide

Introduction to statistics

Question

$The mean and the standard deviation (s.d.) of 10 observations are 20 and 2 respectively.$
$Each of these 10 observations is multiplied by p and then reduced by q, where p \neq 0 and$
$q \neq 0 . If the new mean and new s.d. become half of their original values, then q is equal$ $t o :$

Difficult

A

10
B

-10
C

-20
D

-5

Solution

$If each observation is multiplied with p & then q is subtracted$
$New mean \bar{x_{1}} = p \bar{x} - q \Rightarrow 10 = p (20) - q \dots \dots (1)$
and new standard deviations
$\begin{array}{l} σ_{2} = | p | σ_{1} \Rightarrow 1 = | p | (2) \Rightarrow |p| = \frac{1}{2} \Rightarrow p = \pm \frac{1}{2} \\ If p = \frac{1}{2} then q = 0 (from equation (1)) \\ If p = - \frac{1}{2}, then q = - 20 \end{array}$

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