If 88 is replaced by 93 and 41 is replaced by 47 in the following observations, 46, 48, 63, 76, 88, 41, 35, 55, 90, 56, 92, then
what would be the difference between the new median and the previous median?

Correct option is B

Given:

The original list of numbers:
46, 48, 63, 76, 88, 41, 35, 55, 90, 56, 92.

After replacement:

88 is replaced by 93.

41 is replaced by 47.

Concept Used:

Median is the middle value of a data set when arranged in ascending order.

If the number of observations is odd, the median is the middle number.

If the number of observations is even, the median is the average of the two middle numbers.

Solution:

Original numbers:
46, 48, 63, 76, 88, 41, 35, 55, 90, 56, 92.

Arranging in ascending order:
35, 41, 46, 48, 55, 56, 63, 76, 88, 90, 92.

There are 11 numbers (odd), so the median is the 6th number:

Original median = 56

Replaced numbers:

88 is replaced by 93.

41 is replaced by 47.

New numbers:
46, 48, 63, 76, 93, 47, 35, 55, 90, 56, 92.

Arranging in ascending order:
35, 46, 47, 48, 55, 56, 63, 76, 90, 92, 93.

Again, there are 11 numbers (odd), so the median is the 6th number:

New median = 56

Difference = New median − Original median = 56 - 56 = 0

Thus, the difference between the new median and the previous median is 0.