Lesson 4: Display Data in Frequency Tables and Histograms

Property

To construct a frequency table from a set of raw data:

1. Determine Intervals: Find the range of the data (maximum value - minimum value). Decide on a number of equal-sized, non-overlapping intervals that cover the entire range.
2. Tally Data: Go through the data set one value at a time. Make a tally mark in the row for the interval where each value falls.
3. Count Frequency: Count the tally marks for each interval and write the total in the "Frequency" column.

Examples

Property

A histogram visualizes the distribution of continuous, quantitative data. Instead of showing individual data points, it groups the data into equal-width intervals called bins (or classes).

Rectangles are drawn above each bin to show the frequency of data within that interval. Because the numerical data is continuous, the right side of one rectangle must touch the left side of the next rectangle—there are NO gaps between the bars.

Examples

• Continuous Data (No Gaps): A nurse records resting heart rates. The data is grouped into equal bins: 50-59, 60-69, 70-79, and 80-89. The bars touch each other to show that the numerical scale continues smoothly from one interval to the next.
• Choosing Bin Width: Test scores range from 50 to 100.

Using a bin width of 5 produces 10 narrow bars, showing exactly where scores cluster.
Using a bin width of 25 produces only 2 massive bars, hiding all the detail of the distribution.