Chapter 7.3, Problem 6Q

To determine

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

Answer to Problem 6Q

  

The distribution is skewed left.

Explanation of Solution

Given:

The given data set is:

20,50,60,40,40,30,60,40,50,20,20,35

Calculation:

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

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

  $20,20,20,30,35,40,40,40,50,50,60,60$

Smallest value = 20

Largest value = 60

Lower half = 20, 20, 20, 30, 35, 40

Upper half = 40, 40, 50, 50, 60, 60

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

Quartiles:

  $Q1=\frac{20+30}{2}=25$

  $Q3=\frac{50+50}{2}=50$

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 right side of the plot. The left whisker extends more than the right whisker. Hence, the distribution is skewed left.