JEE MAIN - Mathematics (2022 - 25th June Evening Shift - No. 19)
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
21
Explanation
Mean $$ = {{n{{(n + 1)} \over 2}} \over n} = {{n + 1} \over 2}$$
M.D. $$ = {{2\left( {{{n - 1} \over 2} + {{n - 3} \over 2} + {{n - 5} \over 2} + \,\,\,...\,\,\,0} \right)} \over n} = {{5(n + 1)} \over n}$$
$$ \Rightarrow ((n - 1) + (n - 3) + (n - 5) + \,\,...\,\,0) = 5(n + 1)$$
$$ \Rightarrow \left( {{{n + 1} \over 4}} \right)\,.\,(n - 1) = 5(n + 1)$$
So, $$n = 21$$
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