Question

If a new grade, Y, is added to the data set, so the data set becomes 12, 78, 24, 28, 42, 60, 94, 62, 68, Y (where Y is the new grade), what is the maximum amount by which the new median could differ from the old median (old median = 60).

Answer 1

Median is the middlemost value in the dataset.

Old data set was like this -

12, 24, 28, 42, 60, 62, 68, 78, 94        (afetr arranging in ascending order)

Now, Y is the new grade.

Now the number of observations is 10.

So, median will become the mean of 5 th and 6 th data.

Now, if Y<60, or Y>62 then median will be the mean of 60 and 62 i.e. 61.

Now if Y=0 (or less than 12) then also new median will be 61 and if Y becomes 70 (or greater than 68) then also new median will be 61.

If Y is 60, then new median will also be 60.

If Y is 61, then new median will be mean of 60 and 61 i.e. 60.5

If Y is 62, then new median will be mean of 60 and 62 i.e. 61.

This is the overall possible values of new median for all possible values of Y.

Hope you can understand and appreciate the solution.