# Comparison of Univariate and Bivariate Data

Shodor > Interactivate > Lessons > Comparison of Univariate and Bivariate Data

### Abstract

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.

This lesson is designed for students who are familiar with Shodor applets, particularly Bar Graph, Box Plot, Circle Graph, and Histogram.

### Objectives

Upon completion of this lesson, students will:

• 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.

### Student Prerequisites

• Mathematical: Students must be able to:
• collect and organize data.
• solve for statistical measures such as mean, median, and mode.
• Technological: Students must be able to:
• perform basic mouse manipulations such as point, click and drag
• use a browser for experimenting with the activities

### Teacher Preparation

Students will need

• Paper and pencil
• Copy of worksheet

Teacher will need

### Key Terms

 average 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

1. 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.

2. 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.
3. 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.
• Introduce students to the Multi Bar Graph and Regression applets.
4. Guided Practice
• Work through Sample Problems with students to introduce the types of problems they will be asked to do.
• Have students create the graphs that best fit the data using the following applets:
5. Independent Practice
• 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.
6. 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: 