#### Math - 2019-20

# 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.

*Adopted: 2016*

### 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: May 29, 2019*