Question

Find a whole number that, when added to the data set below, does not change the interquartile range.

18, 20, 22, 26, 27, 28, 30, 34


One possible whole number is__.

Answer 1

Answer: 25 can be an option.

Explanation:

Interquartile range is defined as the difference between the third quartile and the first quartile.

we have 8 values, so the first quartile is the lower 25% of the data:

the 25% of 8 is:

0.25*8 = 2

So the first quartile is 18 + 20 = 38

the third quartile is 30 + 34 = 64.

So we can add any integer that does not affect the first or thid quartile and the interquartile range will remain unchanged, this is if we add a number right in the midle of our data set, for example, we could add a number between 22 and 26 (let's use 25) and the interquartile range will remain unchanged.