The mean and the standard deviation (s.d.) of 10 observations are 20 and 2 resepectively. Each of these 10 observations is multiplied by p and then reduced by q, where p $\ne$ 0 and q $\ne$ 0. If the new mean and new s.d. become half of their original values, then q is equal to
Solution
Let observations are
x<sub>1</sub>, x<sub>2</sub>, ...., x<sub>10</sub>
<br><br>Here mean = 20 and standard deviation(S.D) = 2
<br><br>When each of these 10
observations is multiplied by p then new observations are
px<sub>1</sub>, px<sub>2</sub>, ....., px<sub>10</sub>
<br>and new mean = 20p and new standard deviation(S.D) = 2|p|
<br><br>Now when Reduced by q then new observations are
<br>px<sub>1</sub> - q, px<sub>2</sub> - q, ....., px<sub>10</sub> - q
<br><br>and new mean = 20p - q and new standard deviation(S.D) = 2|p|
<br><br>Given 20p - q = ${{20} \over 2}$ = 10
<br>and 2|p| = ${2 \over 2}$ = 1
<br><br>$\Rightarrow$ p = $\pm$ ${1 \over 2}$
<br><br>If p = ${1 \over 2}$ then q = 0 (not possible as given q $\ne$ 0)
<br><br>If p = - ${1 \over 2}$ then q = -20
About this question
Subject: Mathematics · Chapter: Statistics · Topic: Measures of Central Tendency
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