Chapter 11.2, Problem 9E

To determine

Make a box-and-whisker plot.

Answer to Problem 9E

Median = $4$

  $Q_1=2.5$

  $Q_3=5$

Max = $6$

Min = $0$

Explanation of Solution

Given Information: Hours of television watched: $0,3,4,5,2,4,6,5$

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

Calculation:

Hours of television watched: $0,3,4,5,2,4,6,5$

As, in ascending order

Hours of television watched: $0,2,3,4,4,5,5,6$

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

So,

Median = $\frac{4+4}{2}$

Hence,

Median = $4$

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

So,

  $Q_1=\frac{2+3}{2}$

Hence,

  $Q_1=2.5$

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

So,

  $Q_3=\frac{5+5}{2}$

Hence,

  $Q_3=5$

Max = $6$

Min = $0$