The following lesson is designed to introduce students to the differentiation between univariate
and bivariate data. Students will gain experience determining what types of graphs and measures
are appropriate for each type of data.

This lesson is designed for students who are familiar with graphs and measures related to
univariate data, even if they don't know the vocabulary term.

be able to differentiate between univariate and bivariate data.

understand the different between categorical and numerical data.

understand what type of measure and representations to use for different data types.

Standards Addressed:

Grade 10

Statistics and Probability

The student demonstrates an ability to classify and organize data.

The student demonstrates an ability to analyze data (comparing, explaining, interpreting, evaluating, making predictions, describing trends; drawing, formulating, or justifying conclusions).

Grade 6

Statistics and Probability

The student demonstrates an ability to classify and organize data.

The student demonstrates an ability to analyze data (comparing, explaining, interpreting, evaluating; drawing or justifying conclusions).

Grade 7

Statistics and Probability

The student demonstrates an ability to classify and organize data.

The student demonstrates an ability to analyze data (comparing, explaining, interpreting, evaluating, making predictions; drawing or justifying conclusions).

Grade 8

Statistics and Probability

The student demonstrates an ability to classify and organize data.

The student demonstrates an ability to analyze data (comparing, explaining, interpreting, evaluating, making predictions, describing trends; drawing, formulating, or justifying conclusions).

Grade 9

Statistics and Probability

The student demonstrates an ability to classify and organize data.

The student demonstrates an ability to analyze data (comparing, explaining, interpreting, evaluating, making predictions, describing trends; drawing, formulating, or justifying conclusions).

Grade 7

Statistics, Data Analysis, and Probability

1.0 Students collect, organize, and represent data sets that have one or more variables and identify relationships among variables within a data set by hand and through the use of an electronic spreadsheet software program

Grades 8-12

AP Probability and Statistics

14.0 Students organize and describe distributions of data by using a number of different methods, including frequency tables, histograms, standard line graphs and bar graphs, stem-and-leaf displays, scatterplots, and box-and-whisker plots.

Eighth Grade

Statistics and Probability

Investigate patterns of association in bivariate data.

Statistics and Probability

Interpreting Categorical and Quantitative Data

Summarize, represent, and interpret data on a single count or measurement variable

Summarize, represent, and interpret data on two categorical and quantitative variables

Interpret linear models

Grades 6-8

Data Analysis and Probability

Select and use appropriate statistical methods to analyze data

Grades 9-12

Data Analysis and Probability

Select and use appropriate statistical methods to analyze data

Grade 7

Number and Operations, Measurement, Geometry, Data Analysis and Probability, Algebra

COMPETENCY GOAL 4: The learner will understand and use graphs and data analysis.

Grade 8

Number and Operations, Measurement, Geometry, Data Analysis and Probability, Algebra

COMPETENCY GOAL 4: The learner will understand and use graphs and data analysis.

Introductory Mathematics

Data Analysis and Probability

COMPETENCY GOAL 3: The learner will understand and use graphs and data analysis.

7th Grade

Data Analysis & Probability

The student will understand and apply basic statistical and probability concepts in order to organize and analyze data and to make predictions and conjectures.

8th Grade

Data Analysis & Probability

The student will understand and apply basic statistical and probability concepts in order to organize and analyze data and to make predictions and conjectures.

Algebra II

Data Analysis and Probability

The student will collect, organize, represent, and interpret data; make and evaluate inferences and predictions; present and evaluate arguments based on data analysis; and model situations to determine theoretical and experimental probabilities.

Grade 8

Probability and Statistics

12. The student uses statistical procedures to describe data.

7th Grade

Probability and Statistics

7.17 The student, given a problem situation, will collect, analyze, display, and interpret data, using a variety of graphical methods, including frequency distributions; line plots; histograms; stem-and-leaf plots; box-and-whisker plots; and scattergrams.

Secondary

Probability and Statistics

PS.01 The student will analyze graphical displays of data, including dotplots, stemplots, and histograms, to identify and describe patterns and departures from patterns, using central tendency, spread, clusters, gaps, and outliers. Appropriate technology will be used to create graphical displays.

PS.02 The student will analyze numerical characteristics of univariate data sets to describe patterns and departure from patterns, using mean, median, mode, variance, standard deviation, interquartile range, range, and outliers. Appropriate technology will be used to calculate statistics.

It is better to avoid this sometimes vague term. It usually refers to the (arithmetic) mean, but it can also signify the median, the mode, the geometric mean, and weighted mean, among other things

bar graph

A diagram showing a system of connections or interrelations between two or more things by using bars

mean

The sum of a list of numbers, divided by the total number of numbers in the list. Also called arithmetic mean

median

"Middle value" of a list. The smallest number such that at least half the numbers in the list are no greater than it. If the list has an odd number of entries, the median is the middle entry in the list after sorting the list into increasing order. If the list has an even number of entries, the median is equal to the sum of the two middle (after sorting) numbers divided by two. The median can be estimated from a histogram by finding the smallest number such that the area under the histogram to the left of that number is 50%

mode

For lists, the mode is the most common (frequent) value. A list can have more than one mode. For histograms, a mode is a relative maximum ("bump"). A data set has no mode when all the numbers appear in the data with the same frequency. A data set has multiple modes when two or more values appear with the same frequency.

scatter plot

A graphical representation of the distribution of two random variables as a set of points whose coordinates represent their observed paired values.

Lesson Outline

Focus and Review

Remind students what has been learned in previous lessons and have students review:

Mean

Median

Mode

Range

Box Plots

Bar Graphs

Pie Graphs

Stem and Leaf Plots

Ask students to brainstorm ideas about what univariate, bivariate, and multivariate data might be.
Explain to students that they have already dealt with univariate data without using that
vocabulary term.

Objectives

Let the students know what it is they will be doing and learning today. Say something like this:

Today we are going to discover the differences between two types of data: univariate and
bivariate.

Once we learn about the differences between these types of data, we will determine the
appropriate graphs and measures for each type of data.

We will use the computers later, but please do not open them until I instruct you to do so.

Teacher Input

Lead students in a
discussion about the differences between univariate and bivariate data.

Lead students in a
discussion about the differences between categorical and numerical data. Be sure to talk about how
bivariate data can include both categorical and numerical data and that it can be represented
using a multi-bar graph or scatter plot depending on the type of data.

Provide students with examples of how to display and analyze different types of data.

Have students work in pairs to collect data and complete a
worksheet which asks them to create graphs of different types of data. Students can use the different
applets listed above to create these graphs.

Closure

You may wish to bring the students back together to discuss what applets they choose to use to
represent their data and any problems that we especially hard for the students.

Alternate Outline

This lesson can be rearranged if there is only one available computer:

While working on the worksheet, students can create data representations by hand and they can
choose one graph to create using the appropriate applet and then share the graph with the class.

Suggested Follow-Up

This lesson could be followed by a series of discussion that explore bivariate data in more depth: