JEE MAIN - Mathematics (2022 - 25th July Evening Shift - No. 13)
If the mean deviation about median for the numbers 3, 5, 7, 2k, 12, 16, 21, 24, arranged in the ascending order, is 6 then the median is :
11.5
10.5
12
11
Explanation
Median $$ = {{2k + 12} \over 2} = k + 6$$
Mean deviation $$ = \sum {{{|{x_i} - M|} \over n} = 6} $$
$$ \Rightarrow {{(k + 3) + (k + 1) + (k - 1) + (6 - k) + (6 - k) + (10 - k) + (15 - k) + (18 - k)} \over 8}$$
$$\therefore$$ $${{58 - 2k} \over 8} = 6$$
$$k = 5$$
Median $$ = {{2 \times 5 + 12} \over 2} = 11$$
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