Find the median of the following observations:

46,64,87,41,58,77,35,90,55,92,33

If 92 is replaced by 99 and 41 by 43 in the above data, what will be the new median?

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Solution

46,64,87,41,58,77,35,90,55,92,33

$W r i t i n g i n a s c e n d i n g o r d e r, 33, 35, 41, 46, 55, 58, 64, 77, 87, 90, 92 H e r e n = 11 w h i c h a n o d d n u m b e r ∴ M e d i a n = \frac{n + 1}{2} t h t e r m = \frac{11 + 1}{2} = \frac{12}{2} = 6 t h t e r m = 58$

By replacing 92 by 93 and 41 by 43,then new order will be 33,35,43,46,55,58,64,77,87,90,99.

$∴ M e d i a n = 6 t h t e r m = 58$

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41, 43, 127, 99, 61, 92, 71, 58, 57

58

46, 41, 77, 58, 35, 64, 87, 92, 33, 55, 90.
In the above data, if 41 and 55 are replaced by 61 and 75 respectively, what will be the new median?

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