Chapter 11.2, Problem 10E

To determine

Make a box-and-whisker plot.

Answer to Problem 10E

Median = $20.5$

  $Q_1=17.5$

  $Q_3=22.5$

Max = $25$

Min = $16$

Explanation of Solution

Given Information: Cat lengths (in inches): $16,18,20,25,17,22,23,21$

Formula Used: Median = $\frac{{\left(\frac{n}{2}\right)}^{th}+{\left(\frac{n}{2}+1\right)}^{th}}{2}term$

Calculation:

Cat lengths (in inches): $16,18,20,25,17,22,23,21$

As, in ascending order

Cat lengths (in inches): $16,17,18,20,21,22,23,25$

• Median

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

So,

Median = $\frac{{\left(\frac{8}{2}\right)}^{th}+{\left(\frac{8}{2}+1\right)}^{th}}{2}term$

Now,

Median = $\frac{{\left(4\right)}^{th}+{\left(5\right)}^{th}}{2}term$

As, ${\left(4\right)}^{th}term=20$ and ${\left(5\right)}^{th}term=21$

So,

Median = $\frac{20+21}{2}$

Hence,

Median = $20.5$

The first quartile, denoted by  $Q_1$ , is the median of the lower half of the data set.

So,

  $Q_1=\frac{17+18}{2}$

Hence,

  $Q_1=17.5$

The first quartile, denoted by  $Q_3$ , is the median of the upper half of the data set.

So,

  $Q_3=\frac{22+23}{2}$

Hence,

  $Q_3=22.5$

Max = $25$

Min = $16$