Overview

Students work together to determine if various types of data gathered are categorical (qualitative) or measurement (quantitative) data. The enrichment activity allows students to determine if the measurement data is discrete or continuous.

Objective

Students will be able to distinguish between categorical and measurement data.

Standards Addressed

Mathematics — Data Analysis

Grade 5

Data Collection, Benchmark E

02. Select and use a graph that is appropriate for the type of data to be displayed; e.g., numerical vs. categorical data, discrete vs. continuous data.

 

Grade 8

Data Collection, Benchmark B

03. Differentiate between discrete and continuous data and appropriate ways to represent each.

 

Procedure

1. Photocopy and cut out the labels on the Measurement vs. Continuous Data page. Divide the students into pairs or groups and give each group an envelope that contains the labels.

2. Have a class discussion of the difference between categorical and measurement data.

3. Have each group place the items under the Measurement Data headings or Categorical Data. Remind them that measurement data or amounts of categorical data can be put on a number line.

4. Discuss answers. You can go around the room and have the each group tell you where they put the data and then get some class consensus to each item.

Measurement Data	Categorical Data
Age Time it takes to get to school Temperature Weight Height Grade-point average Unpopped kernels of popcorn in a bag Class size Calories in a hamburger Family size	Pizza toppings Color of a car Dominant hand Letter grades Gender Type of candy Citizenship NFL team

 

5. Review the meaning of discrete and continuous data. Show these number lines:

   Discrete data is data that can be counted. (You can’t have a half a person).

   

   If your data shows that you have six red cars, seven blue cars and three white cars, you can put 6, 7 and 3 on a number line. However, if you are graphing it, the data is car color; therefore, it is categorical data. The axis would show blue, red and white, not the numbers. The numbers would be shown on the vertical axis of a graph.

   Continuous data can be assigned an infinite number of values between whole numbers.

   

    

6. Photocopy the Discrete vs. Continuous Data page and cut out one page of labels per group. Put each set of labels in an envelope and give one envelope to each group. Have the students place the labels under either the Discrete Data or Continuous Data headings.

Discrete Data	Continuous Data
Unpopped kernels of popcorn in a bag Class size Family size Calories in a hamburger Number of people who prefer Guido’s pizza Number of people who got an A on the test Number of Cleveland Browns fans Baskets completed in a minute	Age Weight Height Time it takes to get to school Temperature Grade-point average Calories in a hamburger Arm length

 

7. Talk about the fact that sometimes numbers can be categorical data. For example, the numbers on a football jersey or ZIP codes. Would you want to find the mean, median, mode or range for either of these sets of numbers? This is a tough concept for the kids because you could put them on a number line, but it would be meaningless.

Evaluation

There are 15 items on the student evaluation sheet (giving two points each for the two definitions). Percents could be used if a grade needs to be given.

 

Answers for the Evaluation

1. Measures that have a numerical value and could be placed on a number line

2. Identifies a class or category

3. Quantitative

4. Qualitative

5. a. Categorical
   b. Measurement
   c. Measurement
   d. Categorical
   e. Categorical

6. a. Discrete
   b. Continuous
   c. Discrete
   d. Dontinuous