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Lesson 12-4 Warm-Up

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Stem-and-Leaf Plots (12-4)

stem-and-leaf plot: a chart in which numbers that are partly the same and partly different (in other words, very close together) are broken up into parts called “stems” (the first part of the numbers that is the same) and “leaves” (the second part of the numbers that is different).

Example:

Example: Make a stem and leaf plot of the following set of data.

Step 1: Choose the stems. The least value is 189. The greatest value is 214. Since many of the numbers share the first two numbers, make the first two numbers the stems. In this case, the stems are 18, 19, 20, and 21.

What is a “stem-and-leaf plot”

How do you make a stem-and-leaf plot?

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Stem-and-Leaf Plots (12-4)

Step 2: Draw a stem-and-leaf plot. Make sure to include a key to tell what a number means.

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Stem-and-Leaf Plots (12-4)

Example: The winning times in the Olympic 100 Meter Dash are shown in the table below. Make one stem-and-leaf plot to compare both the men’s and women’s times.

Step 1: Since most (“mode”) of the numbers sh are the same number of seconds, make the seconds the stems and tenths of seconds the leaves.

Step 2: Put the numbers in both sets of data in ascending (going up) order:

Men: 9.8 9.9 9.9 9.9 9.9 10.0 10.0 10.0 10.1 10.1 10.2 10.3 Women: 10.5 10.8 10.8 10.9 10.9 11.0 11.0 11.0 11.1 11.1 11.1 11.4

How can you use a stem-and-leaf plot to compare two sets of data ?

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Stem-and-Leaf Plots (12-4)

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Analysis: This “graph” shows that the men’s times tended to be faster than the women’s times. This can be seen by looking at the measures of central tendency, such as the modes (men’s mode is 9.9 and women’s mode is 11.0 and 11.1) and medians (men’’s median is somewhere in the 10s and women’s is in the 11s).

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Stem-and-Leaf Plots (12-4)

To use a stem-and-leaf plot to find the median of a set of dat, arrange the leaves in order and find the middle leaf(ves). To use a stem-and-leaf plot to find the mode, find the leaf (ves) that appear the most in a row.

A class’s test scores were graphed into the following stem-and- leaf plot. What are the median and mode(s) of the data set?

Median: Find the middle leaf(ves). Since there are 24 leaves, there are 24 data items. That means that the middle two (if an even number), or 12th and 13th values,are the median. In this case, (84 + 84) / 2 = 84, so the median is 84% (middle grade is a “B”)

Mode: Find the leaf (ves) that appear the most in a row. Since the four 8’s with the stem 7 appear the most, then the mode is 78% (“C+” was the grade that occurred the “most”)

How can you use a stem-and-leaf plot to find the median and mode of a set of data?

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Solve.

1. The Quails scored the following points in the basketball games they played this season: 67, 78, 49, 84, 75, 64, 74, 89, 76, 56, 67, 79, 45, 57, 80. Make a stem-and-leaf plot for the data.

LESSON 12-4

Stem-and-Leaf Plots

Lesson Quiz

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2. The monthly precipitation for Gilroy and Ukiah are shown to the right. Draw a back-to-back stem-and-leaf plot for the data. Use the median and mode of each data set to compare the data.

Lesson Quiz

LESSON 12-4

Stem-and-Leaf Plots

The median is 1.05 in. for Gilroy and 2.1 in. for Ukiah, but both cities have a mode of 0.1 in. of precipitation. Ukiah also has a mode of 2.1 in. Based on the measures of central tendency Ukiah tends to have more precipitation than Gilroy. but both cities have dry months.