In a previous course, students learned to construct dot plots and histograms. In this activity, students construct a human dot plot to represent class data, which gives a concrete way to interpret the meaning of this representation. Students reason abstractly and quantitatively (MP2) when they interpret information about their class by answering questions about the data set.

Questions for data collection aren’t printed in the task. They are suggested in the Launch so that they can be customized for each class.

The goal of this activity is to remind students of the process for creating and interpreting dot plots. Ask students questions to help them interpret the human dot plot they created. All answers vary, depending on the data collected from the class. For example, if students answered the question, “How many siblings do you have?” here are sample questions for the data set:

• “How many students have no siblings?” (2)
• “How many students have more than 3 siblings?” (7)
• “How many siblings does [a certain student] have?” ([The certain student] has 1 sibling.)
• “Can we figure out the median number of siblings?” (Yes, the median is _____.)
• “Who has the most siblings here?” ( _____ has the most siblings.)
• “How many siblings do most of your classmates have?” (Most of my classmates have 3 siblings, because that is the number with the highest frequency.)

Each student should work to create the dot plot from the data collected from the class. Students should collaborate with their partner when answering the questions about the data set. Monitor for students’ strategies for expressing the typical amount of sleep (some may calculate mean, and some may calculate median). Highlight that the two ideas of “typical” for a given data set will be emphasized in later lessons.

This activity will help students when they analyze data in a later lesson. It also gives them practice with collecting data from classmates, and representing it with a graph, which is a skill they will use throughout the unit.

Students may think the dots should represent the amount of sleep instead of the number of people who got the same amount of sleep as the corresponding number on the number line. For example, four dots over the number 5 means that four people got 5 hours of sleep. Students sometimes read this as five people getting 4 hours of sleep. The dots represent the frequency of the numbers on the number line. It may help students to label the number line before adding their dots for the data. In this case, the number line should be labeled “hours of sleep” to show that the numbers on the number line represent the amount of sleep rather than the number of people in a category. Students may need guidance on what interval to use when creating their number lines. Remind students of the earlier task and how each dot represented a single student.

The goal of this activity is to make sure students understand the meaning of a dot plot. Here are some sample questions to promote a class discussion:

• “What are similarities and differences between dot plots and box plots?” (Dot plots and box plots both help us find the median, lowest value, and highest value. They are different because a dot plot gives enough information to find the mean, and the box plot does not.)
• “When is a dot plot more useful in representing data?” (A dot plot is more useful if we want to know about the frequency of individual values or see the shape of the distribution. The box plot gives a range of points, so it is not possible to know how many data points are included in the data and how many times.)

The goal of the lesson discussion is for students to connect how dot plots are created with what they show about a data set, and to contrast them with box plots. For example, students might notice that while a dot plot illustrates a distribution more precisely, a box plot shows the median without any further interpretation needed. Discuss how to construct dot plots and when they are useful. Here are sample questions to promote a class discussion:

• “How do dot plots help to analyze data?” (Dot plots show each data point in a data set. They also show the shape of a data distribution.) 
• “What are similarities and differences between dot plots and box plots?” (They both give us information about the distribution of a data set. A dot plot shows where each data point lies along a number line, whereas a box plot shows only the values that split the data set into four quarters.)