Amount of time, in minutes, for nurses to respond to the calls of 50 randomly selected patients. Stem-and-leaf of response N = 50 Leaf Unit = 0.

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1 Stem-and-Leaf Plots Provide a picture of continuous measurement data. Reveal the distribution of the data while retaining the original data. Quick-and-dirty, but can get unwieldy if data are widely dispersed. Example: Basic Stem-and-Leaf Plot Amount of time, in minutes, for nurses to respond to the calls of 50 randomly selected patients. Stem-and-leaf of response N = 50 Leaf Unit = (8) Stem-and-leaf plot of 50 response times. Handout 03 Page 1 of 13

2 How to create a stem-and-leaf plot? 1. Separate each data point into a STEM and a LEAF. The plot should consist of at least 5 stems. Each leaf should consist of one and only one digit. If necessary, TRUNCATE the original data. 2. List the stems vertically in increasing order. Draw a vertical line to the right of the stems. 3. Fill in the stems with their corresponding leaves. 4. If there are fewer than 5 stems, SPLIT the stems. a. Typically, splitting the stems entails listing each stem twice. Then, the first stem contains the leaves 0, 1, 2, 3, 4, and the second stem contains the leaves 5, 6, 7, 8, 9. b. However, one can also split the stems by listing each stem five times. In this case, the first stem contains the leaves 0, 1, the second stem contains the leaves 2, 3,..., and the fifth stem contains the leaves 8, 9. Handout 03 Page 2 of 13

3 How to read Minitab stem-and-leaf plots? N specifies the number of original data points. The stem and leaves are separated by a space. The column of numbers to the left of the stem-and-leaf plot are CUMULATIVE FREQUENCIES for each stem moving from the extreme stems to the center stem. The center stem, which is denoted by parentheses around its frequency, contains the MEDIAN. The number in the parentheses indicates the number of leaves in the center stem. The leaf unit indicates where to place the decimal point when re-creating the original data. In general, first concatenate the stem-and-leaf, and then multiply by the leaf unit. How to create stem-and-leaf plots in Minitab? 1. Select Stat. 2. Select Graph. 3. Select Character Graphs. 4. Select Stem-and-Leaf. 5. The Stem-and-Leaf Pop-Up Window will appear. In the left box, click once on the variable you want analyzed. Click once on Select button. The column name (or variable name) will appear in the box labeled Variables. 6. Select OK. The plot will appear in the Session Window. Handout 03 Page 3 of 13

4 Example: Stem-and Leaf Plot with Too Few Stems Quiz grades of 24 randomly selected students. Stem-and-leaf of C1 N = 24 Leaf Unit = (12) Stem-and-leaf plot of 24 quiz grades. Too few stems. Note: If the stem-and-leaf plot contains too few stems, then it is difficult to understand the distribution of the data. Handout 03 Page 4 of 13

5 Example: Stem-and-Leaf Plot with Split Stems Quiz grades of 24 randomly selected students. Stem-and-leaf of Grades N = 24 Leaf Unit = (2) Stem-and-leaf plot of 24 quiz grades. Handout 03 Page 5 of 13

6 Example: Stem-and-Leaf Plot with Truncated Data Distance, in kilometers, traveled by the debris in 24 randomly selected landslides. Stem-and-leaf of Distance N = 24 Leaf Unit = (6) Stem-and-leaf plot of 24 landslide distances. Handout 03 Page 6 of 13

7 Histograms Provide a picture of continuous measurement data. Most appropriate for large datasets, n > 25, say. Two types: 1) frequency and 2) relative frequency (percent). Description Vertical scale represents frequencies (percentages). Horizontal scale represents continuous variable divided up into equal-sized categories. Bar heights represents the number (percentage) of data points falling into each category. Considerations when Defining Categories: Should not have too few or too many categories. All of the categories should be the same size. Each data point must fall into one and only one category. If a data point falls on a boundary, we will use the convention of placing the data point in the category to the right. Trade-off between meaningfully-defined categories and technically-defined categories. Handout 03 Page 7 of 13

8 Example: Basic Frequency Histogram Age, in years, when adolescent growth spurt began in 35 randomly selected boys. 10 Frequency Age (in years) Frequency histogram of ages of adolescent growth spurt in 35 boys. Handout 03 Page 8 of 13

9 Example: Basic Relative Frequency (Percent) Histogram Age, in years, when adolescent growth spurt began in 35 randomly selected boys Percent Age (in years) Relative frequency (percent) histogram of ages of adolescent growth spurt in 35 boys. Handout 03 Page 9 of 13

10 Example: Percent Histogram with Too Few Categories Age, in years, when adolescent growth spurt began in 35 randomly selected boys Percent Age (in years) Percent histogram of ages of adolescent growth spurt in 35 boys. Handout 03 Page 10 of 13

11 Example: Percent Histogram with Too Many Categories Age, in years, when adolescent growth spurt began in 35 randomly selected boys Percent Age (in years) 16 Percent histogram of ages of adolescent growth spurt in 35 boys. Handout 03 Page 11 of 13

12 Guidelines for creating a histogram 1. Determine the appropriate number of categories, c, based on the number of data points n. Roughly, between 5 and 15 categories. n works well for many datasets, or refer to table in textbook. 2. Determine the category width: width = (maximum - minimum)/c Round up to help make sure each data point falls into only one class. 3. Determine the categories: From Category 1 minimum minimum + width Category 2 end of category 1 end of category 1 + width Category 3 end of category 2 end of category 2 + width Category n end of category n-1 end of category n-1 + width 4. Determine the number (percentage) of data points in each category. 5. Draw histogram. To Note: Creating a worthwhile histogram is more art than science, and therefore often entails trial-and-error. The above are guidelines only. Handout 03 Page 12 of 13

13 How to create a graphics histogram in Minitab? 1. Select Graph. 2. Select Histogram. 3. The Histogram Pop-Up Window will appear. Click once on the variable you want analyzed. Click once on the Select button. The column name (or variable name) will appear in the box labeled Graph Variables. (If you would like a relative frequency histogram rather than the default frequency histogram, click on Options. Click on Percent. Select OK.) 4. Select OK. A new graph window, which contains the histogram, will appear. How to create a character histogram in Minitab? 1. Select Graph. 2. Select Character Graphs. 3. Select Histogram. 4. The Histogram Pop-Up Window will appear. Click once on the variable you want analyzed. Click once on the Select button. The column name (or variable name) will appear in the box labeled Variables. 5. Select OK. A histogram will appear in the Minitab session window. Handout 03 Page 13 of 13