Chapter B.2, Problem 50E

To determine

To construct: The box-and-whisker-plot for both the sets of the data and discuss the differences of both the plots.

Explanation of Solution

Given:

The data set is:

Original design	New Design
15.1	55.8
78.3	71.5
56.3	25.6
68.9	19
30.6	23.1
27.2	37.2
12.5	60
42.7	35.3
72.7	18.9
20.2	80.5
53	46.7
13.5	31.1
11	67.9
18.4	23.5
85.2	99.5
10.8	54
38.3	23.2
85.1	45.5
10	24.8
12.6	87.8

Graph:

The box-and-whisker-plot for original design could be constructed as:

  

Now, box-and-whisker-plot for new design could be constructed as:

  

Interpretation:

From the above constructed plots, it is clear that the distribution of original design is skewed to the right because most of the data is falling on the right side of the plot. On the other hand, the distribution of new design is approximately symmetric which implies the data is taken from the normally distributed population.