In this lesson, students explore various shapes and features of a distribution displayed in a histogram. They use the structure (MP7) to look for symmetry, peaks, clusters, gaps, and any unusual values in histograms. Students also begin to consider how these features might affect how we characterize a data set. For example, how might we describe what is typical in a distribution that shows symmetry? What about in a distribution that has one peak that is not symmetrical? This work is informal, but helps to prepare students to better understand measures of center and spread later in the unit. Students also distinguish between the uses and construction of bar graphs and histograms in this lesson.
- Compare and contrast (orally) bar graphs and histograms, recognizing that descriptions of shape, center, and spread don’t pertain to bar graphs.
- Describe (orally and in writing) the overall shape and features of a distribution represented on a histogram, including peaks, clusters, gaps, and symmetry.
- Identify histograms that display distributions with specific features.
Let's describe distributions displayed in histograms.
Print and cut up cards from the Sorting Histograms blackline master. Prepare 1 set of cards for every 3–4 students.
The Getting to School activity requires students to use data previously collected on their travel methods and times. Organize the data into the tables in the blackline master ahead of time or allow time for students to do it themselves. Either make a copy for every 2 students, or display the completed tables for all to see during the activity.
- I can describe the shape and features of a histogram and explain what they mean in the context of the data.
- I can distinguish histograms and bar graphs.
The center of a set of numerical data is a value in the middle of the distribution. It represents a typical value for the data set.
For example, the center of this distribution of cat weights is between 4.5 and 5 kilograms.
The distribution tells how many times each value occurs in a data set. For example, in the data set blue, blue, green, blue, orange, the distribution is 3 blues, 1 green, and 1 orange.
Here is a dot plot that shows the distribution for the data set 6, 10, 7, 35, 7, 36, 32, 10, 7, 35.
The frequency of a data value is how many times it occurs in the data set.
For example, there were 20 dogs in a park. The table shows the frequency of each color.
color frequency white 4 brown 7 black 3 multi-color 6
A histogram is a way to represent data on a number line. Data values are grouped by ranges. The height of the bar shows how many data values are in that group.
This histogram shows there were 10 people who earned 2 or 3 tickets. We can't tell how many of them earned 2 tickets or how many earned 3. Each bar includes the left-end value but not the right-end value. (There were 5 people who earned 0 or 1 tickets and 13 people who earned 6 or 7 tickets.)
The spread of a set of numerical data tells how far apart the values are.
For example, the dot plots show that the travel times for students in South Africa are more spread out than for New Zealand.