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The median of the following observations 46, 64, 87, 41, 58, 77, 35, 90, 55, 92, 33 is 58. If 92 is replaced by 99 and 41 by 43 in the given data, the
Question

The median of the following observations 46, 64, 87, 41, 58, 77, 35, 90, 55, 92, 33 is 58. If 92 is replaced by 99 and 41 by 43 in the given data, then the new median is:

A.

56.5

B.

55

C.

57.5

D.

58

Correct option is D

Given:
Original observations: 46, 64, 87, 41, 58, 77, 35, 90, 55, 92, 33
Modifications: 92 is replaced by 99, and 41 is replaced by 43.
Formula Used:
For an odd number of observations 'n', Median = Value of the (n+12) (\frac{n+1}{2})​th observation in sorted order.
Solution:
First, let's arrange the modified data in ascending order.
The new set of numbers is: 46, 64, 87, 43, 58, 77, 35, 90, 55, 99, 33
Sorting the new data:
33, 35, 43, 46, 55, 58, 64, 77, 87, 90, 99
The total number of observations is 11, which is odd.
Median position = 11+12\frac{11 + 1}{2}​ = 6th observation.
The 6th observation in the sorted list is 58.
Thus, the new median remains 58.
Final Answer
So the correct answer is (d)

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