Chapter 2, Problem 9CS

In the chapter introduction, we presented gas mileage data for 2016 model year hybrid and small non-hybrid cars. We will use histograms and back-to-back stem-and-leaf plots to compare the mileages between these two groups of cars. The following tables present the mileages, in miles per gallon.

Construct a back-to-back stem-and-leaf plot for these data, using two lines for each stem. Which do you think illustrates the comparison better, the histograms or the back-to-back stem-and-leaf plot? Why?

Compare the histogram for the hybrid cars with the histogram for the non-hybrid cars. For which cars do the mileages vary more?

To determine

To construct and compare:Thehistogramsfor the hybrid andnon-hybrid cars and the back-to-back stem-and-leaf plot for the given data.

Answer to Problem 9CS

Thebetter illustration of comparison is back-to-back stem-and-leaf.

Explanation of Solution

Given information:The gas mileage data for 2016 model year hybrid and small non-hybrid cars is given. The following tables present the mileages, in miles per gallon.

Mileage Ratings for 2016 Hybrid cars
42	31	50	25	31	32	20	30
26	20	31	28	42	21	50	34
29	30	41	29	40	20	42	26
46	29	28	42	40	33	42	28
28	30	37	26	37	44	40	42
50	26	45	41	52	40	38	37
30	21	40	56	34	47	40	26

Mileage Ratings for 2016 Small Non-hybrid cars
37	35	50	36	36	35	34	35
34	34	45	34	36	36	35	35
36	35	35	37	34	35	35	34
40	36	35	36	36	35	37	35
35	36	36	35	34	35	34	37
35	35	36	34	34	35	34	36
50	39	45	44	36	37	35	36

Definition used:Stem plot is a tool to visualize the shape of a distribution.

Calculation:

The back-to-back stem-and-leaf plot for the given data is given by

  $\begin{array}{l}9 9 9 9 8 8 8 8 6 6 2\\ 6 6 6 5 1 1 0 0 0 2\\ 8 7 7 7 4 4 3 2 1 3 4 4 4 4 4 4 4 4 4 4 4 5 5 5 5 5 5 5 5 5 5 5 5 5 5 \\ 1 1 0 0 0 0 3 5 5 5 5 5 6 6 6 6 6 6 6 6 6 6 6 6 6 6 7 7 7 7 7 9 \\ 6 4 2 2 2 2 2 2 1 0 4 0 4 5 5\\ 0 0 0 4\\ 6 2 0 0 0 5 0 0\end{array}$

The table of relative frequency for hybrid cars is given by

Class	Frequency	Relative frequency
20-29	18	0.3214
30-39	15	0.2679
40-49	18	0.3214
50-59	5	0.0893

The relative frequency histogram for hybrid cars is given by

  

The table of relative frequency for non-hybrid cars is given by

Class	Frequency	Relative frequency
31-35	30	$0.5357$
36-40	21	$0.375$
41-45	3	$0.0536$
46-50	2	$0.0375$

The relative frequency histogram for non-hybrid cars is given by

  

From the above two histograms and back-to-back stem-and-leaf plot, the better illustration of comparison is back-to-back stem-and-leaf because it will give a quick visualized comparison of the data by looking the shape of the distribution.