# 5.16 - Stem-and-Leaf Plots

The student, given a practical problem, will

a)  represent data in line plots and stem-and-leaf plots;

b)  interpret data represented in line plots and stem-and-leaf plots; and

c)  compare data represented in a line plot with the same data represented in a stem-and-leaf plot.

### BIG IDEAS

• So that I can use a Stem-and-Leaf plot to organize data making it easier to find the mean, median, mode, and range of a series of numbers
• So that I can collect and organize data when conducting a survey
• So that I can use a line plot to compare peaks in data
• So that I can use a line plot and/or Stem-and-Leaf plot to provide a visual representation of my data

### UNDERSTANDING THE STANDARD

• The emphasis in all work with statistics should be on the analysis of the data and the communication of the analysis, rather than on a single correct answer. Data analysis should include opportunities to describe the data, recognize patterns or trends, and make predictions.
• Statistical investigations should be active, with students formulating questions about something in their environment and determining quantitative ways to answer the questions.
• Investigations that support collecting data can be brief class surveys or more extended projects taking many days.
• Through experiences displaying data in a variety of graphical representations, students learn to select an appropriate representation (i.e., a representation that is more helpful in analyzing and interpreting the data to answer questions and make predictions).
• There are two types of data: categorical and numerical.  Categorical data can be sorted into groups or categories while numerical data are values or observations that can be measured. For example, types of fish caught would be categorical data while weights of fish caught would be numerical data.  While students need to be aware of the differences, they do not have to know the terms for each type of data.
• A line plot shows the frequency of data on a number line. Line plots are used to show the spread of the data and quickly identify the range and mode. • A stem and leaf plot uses columns to display a summary of discrete numerical data while maintaining the individual data points.  A stem-and-leaf plot displays data to show its shape and distribution.

 Stem Leaf 0 3,6,9 1 2,5,7,8 2 4,6 3 1,3,7,7,7 4 0,0,4,8 5 6 1,2,2,3,8 3|5=35

• The data are organized from least to greatest.
• Each value is separated into a stem and a leaf (e.g., two-digit numbers are separated into stems (tens) and leaves (ones)).
• The stems are listed vertically from least to greatest with a line to their right. The leaves are listed horizontally, also from least to greatest, and can be separated by spaces or commas. Every value is recorded, regardless of the number of repeats.  No stem can be skipped.  For example, in the stem and leaf plot above, there are no data for the stem 5; 5 should be listed showing no leaves.
• A key is included to explain how to read the plot.

• Different situations call for different types of graphs.  The way data are displayed is often dependent upon what someone is trying to communicate.
• Comparing different types of representations (e.g., charts graphs, line plots, etc.) provides students an opportunity to learn how different graphs can show different aspects of the same data.  Following construction of representations, students benefit from discussions around what information each representation provides.
• Tables or charts organize the exact data and display numerical information.  They do not show visual comparisons, which generally means it takes longer to understand or to examine trends.
• Bar graphs can be used to compare data easily and see relationships.  They provide a visual display comparing the numerical values of different categories.  The scale of a bar graph may affect how one perceives the data.
• Comparisons, predictions and inferences are made by examining characteristics of a data set displayed in a variety of graphical representations to draw conclusions.
• Sample questions that could be explored in comparing different representations such as a chart to a line plot and a stem-and-leaf plot could include:  In which representation can you quickly identify the mode?  The range?  What predictions can you make?

### ESSENTIALS

The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representations to

• Collect data, using observations (e.g., weather), measurement (e.g., shoe sizes), surveys (e.g.,hours watching television), or experiments (e.g., plant growth). (a)
• Organize the data into a chart or table. (a)
• Represent data in a line plot.  Line plots will have no more than 30 data points. (a)
• Represent data in a stem-and-leaf plot where the stem is listed in ascending order and the leaves are in ascending order, with or without commas between leaves. Stem-and-leaf plots will be limited to no more than 30 data points. (a)
• Title the given graph or identify an appropriate title. (a)
• Interpret data by making observations from line plots and stem-and-leaf plots, describing the characteristics of the data and describing the data as a whole.  One set of data will be represented on a graph. (b)
• Interpret data by making inferences from line plots and stem-and-leaf plots. (b)
• Compare data represented in a line plot with the same data represented in a stem-and-leaf plot. (c)

### KEY VOCABULARY

Updated: Mar 06, 2019