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

Answer:

0.35      

Step-by-step 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 = $\frac{1.4+1.7}{2}$

                                                     = 1.55

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

Now for the greatest value, median =  $\frac{1.7+2.1}{2}$

                                                          = 1.9

Absolute difference between the medians = 1.9 -1.55

                                                                        = 0.35