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

Lesson 2: Histograms

In this Grade 6 lesson from Big Ideas Math, Advanced 1, students learn how to create and interpret histograms, including how to organize data values into equal-sized intervals using frequency tables. The lesson covers constructing histograms from frequency tables, reading bar heights to determine frequencies, and analyzing data distributions to answer questions about ranges and intervals. Students also compare different interval sizes to evaluate which representation best displays a given data set.

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

Reading and Interpreting Basic Histogram Features

Property

A histogram displays data by showing the frequency (how often) values appear in different intervals or bins.
The height of each bar represents the frequency of data in that interval.
Key features to identify include: the highest bar (mode interval), the spread of data (range), and where most data is concentrated.

Examples

Book overview

Jump across lessons in the current chapter without opening the full course modal.

Continue this chapter

Chapter 10: Data Displays

  1. Lesson 1

    Lesson 1: Stem-and-Leaf Plots

  2. Lesson 2Current

    Lesson 2: Histograms

  3. Lesson 3

    Lesson 3: Shapes of Distributions

  4. Lesson 4

    Lesson 4: Box-and-Whisker Plots

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

Reading and Interpreting Basic Histogram Features

Property

A histogram displays data by showing the frequency (how often) values appear in different intervals or bins.
The height of each bar represents the frequency of data in that interval.
Key features to identify include: the highest bar (mode interval), the spread of data (range), and where most data is concentrated.

Examples

Book overview

Jump across lessons in the current chapter without opening the full course modal.

Continue this chapter

Chapter 10: Data Displays

  1. Lesson 1

    Lesson 1: Stem-and-Leaf Plots

  2. Lesson 2Current

    Lesson 2: Histograms

  3. Lesson 3

    Lesson 3: Shapes of Distributions

  4. Lesson 4

    Lesson 4: Box-and-Whisker Plots