Learn on PengiPengi Math (Grade 6)Chapter 7: Statistics and Probability

Lesson 6: Visualizing Data with Dot Plots and Histograms

In this Grade 6 lesson from Pengi Math Chapter 7, students learn how to create and interpret dot plots, histograms, and stem-and-leaf plots as tools for visualizing data. The lesson covers how to identify clusters, gaps, peaks, and outliers within each type of display, along with the advantages and limitations of each method. Students build foundational data analysis skills aligned with their Statistics and Probability unit.

Section 1

Dot Plots

Property

An easy graph to make for numerical data is called a dot plot.
To create a dot plot, first draw a number line and then place a dot above the number line at the location of each data value.
If a value is repeated, this is represented by placing another dot above the previous instance(s) of that value.
This type of graph allows us to identify clusters (data points together in a group), gaps (intervals without any reported values), peaks (data where there are more responses than for nearby values), and outliers (values that are significantly different from the rest of the data).

Examples

  • A group of friends records the number of pets they own: 1, 0, 2, 1, 1, 3, 5. A dot plot would show a peak at 1, a cluster from 0-3, and a gap before the value at 5.
  • Students' quiz scores are: 8, 9, 10, 7, 9, 9, 8. The dot plot for this data shows a peak at 9, indicating it's the most frequent score, and all data is clustered between 7 and 10.
  • The number of goals scored in 7 soccer games was: 2, 3, 0, 1, 3, 2, 3. The dot plot has a peak at 3, showing it was the most common number of goals scored in a game.

Explanation

Dot plots are perfect for smaller sets of data. They let you see every single data point at a glance, making it easy to spot where data clumps together (clusters) or where the most common value is (peak).

Section 2

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.

Lesson overview

Expand to review the lesson summary and core properties.

Expand

Section 1

Dot Plots

Property

An easy graph to make for numerical data is called a dot plot.
To create a dot plot, first draw a number line and then place a dot above the number line at the location of each data value.
If a value is repeated, this is represented by placing another dot above the previous instance(s) of that value.
This type of graph allows us to identify clusters (data points together in a group), gaps (intervals without any reported values), peaks (data where there are more responses than for nearby values), and outliers (values that are significantly different from the rest of the data).

Examples

  • A group of friends records the number of pets they own: 1, 0, 2, 1, 1, 3, 5. A dot plot would show a peak at 1, a cluster from 0-3, and a gap before the value at 5.
  • Students' quiz scores are: 8, 9, 10, 7, 9, 9, 8. The dot plot for this data shows a peak at 9, indicating it's the most frequent score, and all data is clustered between 7 and 10.
  • The number of goals scored in 7 soccer games was: 2, 3, 0, 1, 3, 2, 3. The dot plot has a peak at 3, showing it was the most common number of goals scored in a game.

Explanation

Dot plots are perfect for smaller sets of data. They let you see every single data point at a glance, making it easy to spot where data clumps together (clusters) or where the most common value is (peak).

Section 2

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.