Exploring Histograms

The interactive data analysis tool in this investigation allows students to create their own sets of data and examine how various statistical functions such as mean, median, and standard deviation depend on the choice of data.

Instructions for Using the Interactive Tool

To use this interactive tool:

• Entering and editing data: Enter data by clicking in the "Data Input" box; type the value and press "Enter" on the keyboard. To edit data, select a data value by clicking on it and either delete the value or enter a new one. You can order your data values by checking the Order Data box. Use the slider to change the length of the intervals used to create the histogram.

• Looking at the histogram: When you click on a particular bar on the histogram, the percentage of data values represented by that bar is displayed. Place the mouse cursor along the bottom axis to reveal the values determining the endpoints of each interval.

• Summary statistics: In the Summary Statistics box, the length of the intervals, the number of data points, as well as the mean, median, and the standard deviation are displayed.

Below the interactive tool are two sample activities that students can use to learn about statistics. Both activities in this investigation make use of the interactive tool.

Sample Activity 1

• Clear any previous data.
• Enter the numbers 2,3, 4, 4, and 5 into the bar chart.
• Note the summary statistics. What is the value of the mean? The median?
• Describe the shape of the histogram. Which of the following is easily "seen" on the histogram: mean, median, or mode?
• Now enter 77.
• What happened to the mean? To the median? To the mode?
• How does the histogram change?
• What happens to the shape of the bar chart if you change the width of the bars?

Sample Activity 2

• Clear any previous data.
• Enter the numbers 2, 3, 4, 4, and 5 using "Data Input."
• Note the summary statistics. What is the value of the mean? The median?
• Describe the shape of the histogram. What is the value of the mode?
• Now repeatedly enter the number 5.
• What happened to the mean? To the median? To the mode?
• How does the histogram change?
• What happens to the shape of the histogram if you change the length of the intervals?

Real-Life Data

Students should collect or research data which can be entered into the Histogram Tool

Alternatively, students may use the Histogram Tool for their data.

Histogram Tool

This Tool provides several types of data which has already been collected. Students can click on the drop-down menu to select the data they will use for their own histogram.

Sample data includes:

Colleges' SAT Scores
NBA Team Payrolls in 2000
Horsepower of Cars
Bodyfat Percent of 252 Men
Spending Per Student in Some Schools
Gas Mileage for Year 2000 Cars

Alternatively, students may select the "My Data" option and enter their own data. Students may work in pairs or groups of three for this activity.

Other types of data which students could collect or research online include:

Amount of Time Spent on Homework
Points Scored by Individual Basketball Players in a Given Season
Touchdowns Scored, Per Game, by an NFL Team in One Season

At the conclusion of the lesson, students may print out color copies of their histograms to share with their classmates and discuss their findings.