Question

Add three data values to the following data set so the mean increases by 10 and the median does not change. {42, 37, 32, 29, 20}

Answer 1

Sum of the numbers in the set: 42+37+32+29+20 =160

Current mean: 160/5 = 32

Median = the valvue of the middle = 32.

New mean: 32+10= 42.

Sum of numbers in the new set = 42*8 = 336

Difference: 336 - 160 = 176

I want to include 32, so that the new median stays in 32.

So the other two numbers must add 176 - 32 = 144

I will use a smaller number than 32 and the other greater (again in order to  keep the same median.

I will choose 28 and 144 - 28 = 116.

So my three new numbers are 28, 32 and 116 and the new set is {116, 42, 37, 32, 32, 29,28, 20}

Checking:

Sum of the terms: 116+42+37+32+32+29+28+20 = 336

Mean = 336 / 8 = 42, which is 10 more than the original mean.

And the new median is (32+32)/2 = 32. The same of the original set.