QJEEM11Ma21e3: JEE Main 2011 Mathematics - Class 11 JEEM11Ma21e3 Solution: If the mean deviation about the median of the numbers a,…

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If the mean deviation about the median of the numbers a, 2a,........., 50a is 50, then |a| equals

Accepted Answer

NOTE :

If total no of terms are even then median

= {1 \over 2}

[

{n \over 2}

th term

+ \left( {{n \over 2} + 1} \right)

th term]

Here total terms

= 50,

which is even

\therefore

\,\,\,

Median

= {1 \over 2}

[

{{50} \over 2}

th term

+ \left( {{{50} \over 2} + 1} \right)

th term]

= {1 \over 2}

[

25

th term

+

26

th term ]

= {1 \over 2}

[

25a

+

26a

]

=25.5a

Mean deviation (M.D.) about the median

= {{\sum\limits_{i = 1}^{50} {\left| {{x_i} - Median} \right|} } \over N} = 50

(given)

\therefore

{1 \over {50}}\left[ {2 \times \left| a \right| \times \left( {0.5 + 1.5 + 2.5 + ....24.5} \right)} \right] = 50

\Rightarrow 2\left| a \right| \times {{25} \over 2} \times 25 = 2500

\Rightarrow \left| a \right| = {{2500} \over {25 \times 25}} = 4

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