Chapter 2.3, Problem 17E

BMW prices: The following table presents the manufacturer’s suggested retail price (in $1000s) for 2003 base models and styles of BMW automobiles.

Source: autos.yahoo.com

1. Round the data to the nearest whole number (round .5 up) and construct a stem-and-leaf plot, using the numbers 3 through 14 as the stems.
2. Repeat part (a), but split the stems, using two lines for each stem.
3. Which stem-and-leaf plot do you think is more appropriate for these data, the one in part (a) or the one in part (b)’ Why?

To determine

To construct: A stem-and-leaf plot, using the numbers 3 through 14 as the stems by rounding the data to the nearest whole number.

Explanation of Solution

Given information:The following table presents the manufacturer’s suggested retail price for 2003 base models and styles of BMW automobiles.

50.1	89.8	55.2	90.5	30.8	62.7	38.9
70.4	48.0	89.2	47.5	86.2	53.4	90.2
55.2	93.5	39.3	73.6	60.1	140.7	31.2
64.2	44.1	80.6	38.6	68.8	32.5	64.2
56.7	96.7	36.9	65.0	59.8	114.7	43.3
74.9	57.7	108.4	47.4	82.4	44.0	77.6
55.7	93.7	47.5	86.8

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

Calculation:

Rounding the data to the nearest whole number as follows:

50	90	55	91	31	63	39
70	48	89	48	86	53	90
55	94	39	74	60	141	31
64	44	81	39	69	33	64
57	97	37	65	60	115	43
75	58	108	47	82	44	78
56	94	48	87

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

  $\begin{array}{l}3 1137999\\ 4 3447888\\ 5 0355678\\ 6 0034459\\ 7 0458\\ 8 12679\\ 9 001447\\ 10 8\\ 11 5\\ 12\\ 13\\ 14 1\end{array}$

To determine

To construct: A stem-and-leaf plot, using the numbers 3 through 14 as the stems by rounding the data to the nearest whole number and to split the stems using twolines for each stem.

Explanation of Solution

Given information: The following table presents the manufacturer’s suggested retail price for 2003 base models and styles of BMW automobiles.

50.1	89.8	55.2	90.5	30.8	62.7	38.9
70.4	48.0	89.2	47.5	86.2	53.4	90.2
55.2	93.5	39.3	73.6	60.1	140.7	31.2
64.2	44.1	80.6	38.6	68.8	32.5	64.2
56.7	96.7	36.9	65.0	59.8	114.7	43.3
74.9	57.7	108.4	47.4	82.4	44.0	77.6
55.7	93.7	47.5	86.8

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

Calculation:

Rounding the data to the nearest whole number as follows:

50	90	55	91	31	63	39
70	48	89	48	86	53	90
55	94	39	74	60	141	31
64	44	81	39	69	33	64
57	97	37	65	60	115	43
75	58	108	47	82	44	78
56	94	48	87

Now the stem-and-leaf plot for the given data by splitting the stem using two lines for each stem is given by

  $\begin{array}{l}3 113\\ 3 7999\\ 4 344\\ 4 7888\\ 5 03\\ 5 55678\\ 6 00344\\ 6 59\\ 7 04\\ 7 58\\ 8 12\\ 8 679\\ 9 00144\\ 9 7\\ 10 \\ 10 8\\ 11 \\ 11 5\\ 12\\ 12\\ 13\\ 13\\ 14 1\\ 14\end{array}$

To determine

To find:The stem-and-leaf plot which is more appropriate for the data.

Answer to Problem 17E

The part (a) stem-and-leaf plot is more appropriate because part (b).

Explanation of Solution

Given information:The following table presents the manufacturer’s suggested retail price for 2003 base models and styles of BMW automobiles.

50.1	89.8	55.2	90.5	30.8	62.7	38.9
70.4	48.0	89.2	47.5	86.2	53.4	90.2
55.2	93.5	39.3	73.6	60.1	140.7	31.2
64.2	44.1	80.6	38.6	68.8	32.5	64.2
56.7	96.7	36.9	65.0	59.8	114.7	43.3
74.9	57.7	108.4	47.4	82.4	44.0	77.6
55.7	93.7	47.5	86.8

From the stem-and-leaf plot above two parts (a) and (b), the part (a) stem-and-leaf plot is more appropriate because part (b) has too many stems with no leaves.

The stem-and-leaf plot in part (a) shows that most prices are in the 30’s, 40’s and 50’s and that the data is skewed to the right.