The mathematical purpose of the lesson is to represent and interpret data using data displays in a less scaffolded way than in the previous lesson. The work of this lesson connects to previous work done in grade 6 where students summarized and described distributions. The work of this lesson connects to future work because students will use data displays to more formally describe the shape of distributions, and to determine the appropriate measure of center and measure of variability for a given distribution. When students create and interpret a data display, they are reasoning abstractly and quantitatively (MP2) because they are creating a display and interpreting the meaning of the quantities in the display. Additionally, students make use of structure (MP7) to notice differences in distributions with the same shape, but different centers.
- Create and critique graphical representations of student collected data.
- Let’s make, compare, and interpret data displays.
Students will need the numerical data that they collected from a statistical question in a previous lesson. Students will need tools to create and display a dot plot and a box plot to the whole class.
- I can graphically represent the data I collected and critique the representations of others.
Categorical data are data where the values are categories. For example, the breeds of 10 different dogs are categorical data. Another example is the colors of 100 different flowers.
For a numerical or categorical data set, the distribution tells you how many of each value or each category there are in the data set.
The five-number summary of a data set consists of the minimum, the three quartiles, and the maximum. It is often indicated by a box plot like the one shown, where the minimum is 2, the three quartiles are 4, 4.5, and 6.5, and the maximum is 9.
A non-statistical question is a question which can be answered by a specific measurement or procedure where no variability is anticipated, for example:
- How high is that building?
- If I run at 2 meters per second, how long will it take me to run 100 meters?
Numerical data, also called measurement or quantitative data, are data where the values are numbers, measurements, or quantities. For example, the weights of 10 different dogs are numerical data.
A statistical question is a question that can only be answered by using data and where we expect the data to have variability, for example:
- Who is the most popular musical artist at your school?
- When do students in your class typically eat dinner?
- Which classroom in your school has the most books?