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Clarifications: Each clarification provides an explanation of the indicator/objective to help teachers better understand the concept. Classroom examples are often included to further illustrate the concept. While classroom examples could be shared with the students, the intended audience for the explanation/clarification is the classroom teacher-not the student. In addition, classroom examples may or may not reflect the assessment limits.

Standard 4.0 Knowledge of Statistics

Topic A. Data Displays

Indicator 1. Organize and display data

Objective a. Organize and display data using back-to-back stem-and-leaf plots

Assessment limit: Use no more than 20 data points using whole numbers (0–99)

Clarification

A stem-and-leaf plot is a data display that organizes and shows all individual values within a data set, usually organized from least to greatest.

The advantages of organizing data using a stem-and-leaf plot are that it shows:

  • Largest and smallest values and the distribution of the data
  • Clusters and gaps in the data
  • Outliers (values that are widely separated from the rest of the data) in the data set
  • The relative position in the data set of any single value, as each value is represented on the stem-and-leaf plot (unlike a bar graph or a histogram)

The components of a stem-and-leaf plot are:

  • Stem: The stem digits are the ones with the greater place value, as shown below
  • Leaf: The leaf digits are the ones with the lesser place value, as shown below
  • Key: Explains the stem values and the leaf values
  • Title: Describes the data displayed
  • Leaf Headings: For the back-to-back stem-and-leaf plot, each leaf heading shows a subtitle for the data

Example of a stem-and-leaf plot

Number of trees per acre in the forest: 27, 19, 15, 32, 28, 24, 17, 30, and 32

chart image

A back-to-back stem-and-leaf plot compares two data sets. Creating a back-to-back stem-and-leaf plot allows comparison of two different data sets using the same stems.

Classroom Example 1

The following table shows high/low temperatures for selected world cities on July 30, 2004. (Sources: Accu-Weather, Inc. and National Weather Service)

City Athens Brussels Copenhagen Dublin Rome Beijing New Delhi Singapore
High/Low
Temp		 86/67 82/59 76/61 68/52 84/63 86/70 95/79 89/77
 
City Tokyo Manila Buenos Aires Caracas Johannesburg Lima Rio de Janeiro
High/Low
Temp		 85/73 89/77 57/45 79/63 69/42 66/59 72/60

 
Create a back-to-back stem-and-leaf plot for these data sets.

Answer:

Temperatures in Fifteen Cities on July 30, 2004 (Title)

chart image

Note: On each leaf side of the back-to-back stem-and-leaf plot, the data points are always in order from least to greatest starting at the stem. The data points on the left side of the stem are in increasing order from right to left and the data points on the right side of the stem are in increasing order from left to right.

Resource utilized: Exploring Data, James M. Landwehr and Ann E. Watkins, Dale Seymour Publications, 1986.
/instruction/clarification/mathematics/grade7/xml/4A1a.xml
Resources for Objective 4.A.1.a:
CLARIFICATIONS | Sample Assessments |