If the mean deviation about the mean of the numbers 1, 2, 3, .........., n, where n is odd, is ${{5(n + 1)} \over n}$, then n is equal to ______________.
Answer (integer)
21
Solution
<p>Mean $= {{n{{(n + 1)} \over 2}} \over n} = {{n + 1} \over 2}$</p>
<p>M.D. $$ = {{2\left( {{{n - 1} \over 2} + {{n - 3} \over 2} + {{n - 5} \over 2} + \,\,\,...\,\,\,0} \right)} \over n} = {{5(n + 1)} \over n}$$</p>
<p>$\Rightarrow ((n - 1) + (n - 3) + (n - 5) + \,\,...\,\,0) = 5(n + 1)$</p>
<p>$\Rightarrow \left( {{{n + 1} \over 4}} \right)\,.\,(n - 1) = 5(n + 1)$</p>
<p>So, $n = 21$</p>
About this question
Subject: Mathematics · Chapter: Statistics · Topic: Measures of Central Tendency
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