Chapter 11.2, Problem 22E

To determine

To determine the data set.

Answer to Problem 22E

Data Set = $3,4,10,11,15,18$

Explanation of Solution

Given Information: Box-and-whisker plot.

Formula Used:Data Set = Min, $Q_1$ , Median, $Q_3$ , Max and Median = $\frac{{\left(\frac{n}{2}\right)}^{th}+{\left(\frac{n}{2}+1\right)}^{th}}{2}term$

Calculation:

  

Data Set = Min, $Q_1$ , Median, $Q_3$ , Max

As per Box-and-whisker plot,

Median = $10.5$

  $Q_1=4$

  $Q_3=15$

Max = $18$

Min = $3$

• Median

Median for even numbers = $\frac{{\left(\frac{n}{2}\right)}^{th}+{\left(\frac{n}{2}+1\right)}^{th}}{2}term$

So,

Median = $\frac{{\left(\frac{6}{2}\right)}^{th}+{\left(\frac{6}{2}+1\right)}^{th}}{2}term$

Now,

Median = $\frac{{\left(3\right)}^{rd}+{\left(4\right)}^{th}}{2}term$

As, ${\left(3\right)}^{rd}term=10$ and ${\left(4\right)}^{th}term=11$

Now,

Median = $\frac{10+11}{2}$

Hence,

Median = $10.5$

Now, put the values of Min, $Q_1$ , Median, $Q_3$ , Max

Data Set = $3,4,10,11,15,18$