Question

Let Q = {1.7, 1.1, 1.4, 2.1, 2.3, s}. What is the absolute difference between the greatest and least possible values of the median of set Q? Express your answer as a decimal to the nearest hundredth.

Answer 1

0.35

Explanation:

After arranging Q in ascending order excluding s, we get

Q = {1.1,1.4,1.7,2.1,2.3}

Here, the median is 1.7. Now, if s< 1.7,

Q= {1.1,s,1.4,1.7,2.1,2.3}

Now for the least value, median =
`(1.4+1.7)/(2)`

= 1.55

If s>1.7, Q = {1.1,1.4,1.7,2.1,s,2.3,}

Now for the greatest value, median =
`(1.7+2.1)/(2)`

= 1.9

Absolute difference between the medians = 1.9 -1.55

= 0.35