Learn on PengiBig Ideas Math, Course 1Chapter 10: Data Displays

Lesson 2: Histograms

In this Grade 6 lesson from Big Ideas Math Course 1, students learn how to organize data using frequency tables and histograms, including how to select equal-sized intervals and plot bar heights that represent the frequency of values within each interval. Students practice making and interpreting histograms using real-world data, such as laps completed in swimming and paper airplane flight distances, while exploring how different interval choices affect the appearance and clarity of a graph. The lesson aligns with Common Core standards 6.SP.2 and 6.SP.4.

Section 1

Histograms: Bins and Continuous Data

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.

Section 2

Comparing Histograms with Other Data Displays

Property

Choose data displays based on purpose:
dot plots for individual values and identifying clusters/outliers;
histograms for frequency distributions and data shape;
box plots for comparing center and spread across datasets.

Examples

Section 3

Drawing Conclusions from Histograms

Property

To draw conclusions from histograms, analyze the shape, center, and spread of the distribution to understand patterns in the data.
Look for the overall shape (symmetric, skewed left, skewed right, or uniform), identify where most data values are concentrated, observe how spread out the data is, and note any gaps or unusual features.
Use these observations along with the context to make meaningful interpretations about what the data represents.

Examples

Lesson overview

Expand to review the lesson summary and core properties.

Expand

Section 1

Histograms: Bins and Continuous Data

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.

Section 2

Comparing Histograms with Other Data Displays

Property

Choose data displays based on purpose:
dot plots for individual values and identifying clusters/outliers;
histograms for frequency distributions and data shape;
box plots for comparing center and spread across datasets.

Examples

Section 3

Drawing Conclusions from Histograms

Property

To draw conclusions from histograms, analyze the shape, center, and spread of the distribution to understand patterns in the data.
Look for the overall shape (symmetric, skewed left, skewed right, or uniform), identify where most data values are concentrated, observe how spread out the data is, and note any gaps or unusual features.
Use these observations along with the context to make meaningful interpretations about what the data represents.

Examples