Chapter 7.3, Problem 5Q

To determine

The box-and-whisker plot for the given data.

Answer to Problem 5Q

  

The distribution is skewed right.

Explanation of Solution

Given:

The given data set is:

60,15,25,20,55,70,40,30

Calculation:

To draw the box-and-whisker plot for the given data:

Step 1: Arrange the data in ascending order. Calculate median and quartiles.

  $15,20,25,30,40,55,60,70$

Smallest value = 15

Largest value = 70

Lower half = 15, 20, 25, 30

Upper half = 40, 55, 60, 70

Median = $\frac{30+40}{2}=35$

Quartiles:

  $\begin{array}{l}Q1=\frac{20+25}{2}=22.5\\ Q3=\frac{55+60}{2}=57.5\end{array}$

Step 2: Draw a number line with the smallest and largest value. Graph the points above the number line for 5-number summary.

Step 3: Finally, draw a box with Q1 and Q3. Make a line through the median value. Also, make a whisker from the box to the smallest and the largest values.

  

Looking at the box-and-whisker plot, majority of the data is on the left side of the plot. The right whisker extends more than the left whisker. Hence, the distribution is skewed right.