2.2b(vi) Stem-and-Leaf Plots

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2.2b(vi) Stem-and-Leaf Plots

Constructing a Stem and-Leaf Plot‑1. Create two columns, one on the left for stems and one on the right for leaves. 2. List each stem that occurs in the data set in numerical order. Each stem is normally listed only once; however, the stems are sometimes listed two

or more times if splitting the leaves would make the data set’s features clearer.






Stem-and-Leaf Plots

Constructing a Stem and-Leaf Plot (cont.)‑3. List each leaf next to its stem. Each leaf will be listed as many times as it occurs in the original data set.

There should be as many leaves as there are data values. Be sure to line up the leaves in straight columns so that the table is visually accurate.

4. Create a key to guide interpretation of the stem and-leaf plot‑ . 5. If desired, put the leaves in numerical order to

create an ordered stem-and-leaf plot.






Example 2.15: Creating a Stem-and-Leaf Plot

Create a stem-and-leaf plot of the following ACT scores from a group of college freshmen.

ACT Scores

18

27

35

18

23

26

27

17

24

22

29

21

31

32

24

25

19

18

20

26






Example 2.15: Creating a Stem-and-Leaf Plot (cont.)

SolutionACT Scores

Stem Leaves

123

8 9 8 8 73 4 7 6 2 7 9 4 0 1 5 61 2 5

Key: 1|8 = 18






Example 2.16: Creating and Interpreting a Stem-and-Leaf Plot

Create a stem-and-leaf plot for the following starting salaries for entry-level accountants at public accounting firms. Use the stem-and-leaf plot that you create to answer the following questions.

Starting Salaries for Entry-Level Accountants $51,500

$45,500

$45,800

$43,000

$42,900

$44,500

$48,300

$42,500

$46,300

$42,700

$46,500

$47,900

$40,900

$44,200

$50,000

$49,000

$47,700

$45,300

$40,700

$46,400

$50,700

$46,700

$48,000

$46,100

$48,200

$48,600

$44,300

$43,200

$46,300

$45,000






Example 2.16: Creating and Interpreting a Stem-and-Leaf Plot (cont.)

a. What were the smallest and largest salaries recorded? b. Which salary appears the most often? c. How many salaries were in the range $41,000 –

$41,900? d. In which salary range did the most salaries lie:

$40,000–$44,900, $45,000–$49,900, or $50,000 and above?







SolutionThis example is different than Example 2.15 in that the data have more than two digits and every data value ends in two zeros. It is important to choose the stems of the numbers so that the last significant digit in each data point will be the leaf in the chart. Listing the zeros as the leaves for each different stem would be of little use to anyone interpreting the stem-and-leaf plot. Instead, the key will denote that the salaries listed are in hundreds.







Using the first two digits of each salary as a stem, we have the following plot. (Note: It is helpful to first list the salaries in numerical order.)













a. The smallest salary is $40,700; the largest salary is $51,500. b. $46,300 appears twice, which is more than any

other salary. c. No salaries are in the range $41,000–$41,900

because there are no leaves listed for the stem 41. d. By counting the leaves in the given groups, we see that there are more salaries in the range $45,000– $49,900.






Summary

Type of Graph Definition

Pie Chart

Bar Graph

A pie chart shows how large each category is in relation to the whole; that is, it uses the relative frequencies from the frequency distribution to divide the “pie” into different-sized wedges. It can only be used to display qualitative data.

In a bar graph, bars are used to represent the amount of data in each category; one axis displays the categories of qualitative data and the other axis displays the frequencies.

Qualitative Data






Summary (cont.)


Pareto Chart

Side-by-Side Bar Graph

A Pareto chart is a bar graph with the bars in descending order of frequency. Pareto charts are typically used with nominal data.

A side-by-side bar graph is a bar graph that compares the same categories for different groups.

Qualitative Data (cont.)






Summary (cont.)


Stacked Bar Graph

A stacked bar graph is a bar graph that compares the same categories for different groups and shows category totals.

Qualitative Data (cont.)






Summary (cont.)

Quantitative DataType of Graph Definition

Histogram

Frequency Polygon

A histogram is a bar graph of a frequency distribution of quantitative data; the horizontal axis is a number line.

A frequency polygon is a visual display of the frequency of each class of quantitative data that uses straight lines to connect points plotted above the class midpoints.






Summary (cont.)


Ogive

Stem-and-Leaf Plot

An ogive displays the cumulative frequency of each class of quantitative data by using straight lines to connect points plotted above the upper class boundaries.

A stem-and-leaf plot retains the original data; the leaves are the last significant digit in each data value and the stems are the remaining digits.

Quantitative Data (cont.)

Stem Leaves

32 3334

0 7 7 7 80 0 0 0






Summary (cont.)


Dot Plot

Line Graph

A dot plot retains the original data by plotting a dot above each data value on a number line.

A line graph uses straight lines to connect points plotted at the value of each measurement above the time it was taken.

Quantitative Data (cont.)

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2.2b(vi) Stem-and-Leaf Plots