What you should learn

To display and interpret data on a stem-and-leaf plot

NCTM Curriculm Standards 2, 5 - 10

 

In doing this the teacher wants to make sure that the following words are incorporated into the introductory lesson:

Data

Statistics

Stem-and-Leaf Plot

Introduction: Carmela Perez sells artificial joints to hospitals. She often works with the doctors who perform operations to replace joints. So, Ms. Perez does a lot of driving. She needs to buy a new car to replace her current car. Before deciding which car to buy, she wants to find out the miles-per-gallon (MPG) ratios of the cars she likes. The MPG ratios for 25 cars are listed below.

31, 30, 28, 26, 22, 31, 26, 34, 47, 32, 18, 33, 26, 23, 18, 29, 13, 40, 31, 42, 17, 22, 50, 12, 41

Which MPG ratio occurs most frequently? Which is the highest MPG ratio? Which is the lowest?

Each day when you read newspapers or magazines, watch television, or listen to the radio, you are bombarded with numerical information about food, sports, the economy, politics, and so on. Interpreting this numberical information, or data, is important to your understanding of the world around you. A branch of mathemtaics called statistics helps provide you with methods of colledcting, organizing, and interpreting data.

Graphs are often used to display data. The misuse of graphs can lead to false assumptions. One way that graphs are often used to mislead the reader is by labeling the vertical and horizonal scales inconsistently. All of the interval marks should represent the same units. If either of the scales does not begin at zero, this should be indicated by a broken or jagged line.

Another way to organize and display data is by using a stem-and-leaf plot. In a stem-and-leaf plot, the greatest common place value of the data is used to form the stems. The numbers in the next greatest place-value positionare then used to form the leaves. In the list above, the greatest place value is tens. Thus, 31 miles per gallon would have stem 3 and leaf 1.

To make the stem-and-leaf plot, first make a vertical list of the stems. Since the mileage data range from 12 to 50, the stems range from 1 to 5. Then, plot each number by placing the units digit (leaf) to the right of its correct stem. Thus, the milage 31 is plotted by placing leaf 1 to the right of stem 3. Include a key with the plot. The complete stem-and-leaf plot is shown below.

A second stem-and leaf plot can be made to arrange the leaves in numerical order from least to greatest as shown below. This will make it easier for Ms. Perez to analyze the data.

Exercise 1: Use the information in the stem-and-leaf plots above to answer teach question.

a. Which MPG ratio did Ms. Perez plot most frequently?

26 and 31 (each plotted three times)

b. What are the highest and lowest MPG ratios?

c. Each line of the stem-and-leaf plot represents an interval of the data. In which milage interval did Ms. Perez find the most cars?

d. How many cars have a ratio of between 20 and 30 miles per gallon?

e. If you were Ms. Perez, which cars might you investigate more closely? Why?

 

Sometimes the data for a stem-and-leaf plot are numbers that mostly begin with the same digit. In this case, use the digits int he first two places to form the stems.

Exercise 2: The weights (in pounds) of the students in a health and nutrition class are listed below. Make a stem-and-leaf plot of the students weights and answer the questions.

102, 117, 119, 147, 135, 148, 122, 137, 103, 116, 147, 152, 117, 149, 108, 123, 130, 123, 147, 112, 133, 99, 101, 135, 138, 155, 118, 142, 103, 159, 131, 137, 156, 149, 120, 98

Since the data range from 159 to 98 pounds, the stems range from 15 to 9.

a. What does 14|8 represent on the plot?

b. Which interval has the most students in it?

c. What is the difference between the lowest and highest weight?

d. Which weight occurred most frequently?

A back-to-back stem-and-leaf plot can also be used to compare two related sets of data.

Exercise 3: Kyle and Mikito wanted to compare boys' and girls' heights. They measured the height (in inches) of every studnet in their class. The data they collected and stem-and-leaf plot they made are shown below.

In this case, the heights of the boys and the heights of the girls are to be compared. To compare these numbers most effectively, use a back-to-back stem-and-leaf plot.

a. What is the height of the shortest boy? The shortest girl?

b. What is the difference in the height between the shortesst boy and the tallest girl?

c. What does 6|3 represent on each plot?

d. What is the greatest number of boys who are the same height? What is the greatest number of girls who are the same height?

e. What patterns, if any, do you see in the data?

Closing Activity: Check for understanding by using this as a quick review before class is over. It should take about the last five to ten minutes. I would use it for my students as their 'ticket out the door'. Click Here.

Homework: The homework to be assigned for tonight would be: 11 - 25 odd, 27 - 31

Alternative Homework: Enriched: 12 - 22 even, 23 - 31

Extra Practice: Students book page 757 Lesson 1-4

Extra Practice Worksheet: Click Here.

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