Middle School Math Lesson: Identifying Statistical Questions and Determining Median and Range
Objective: Students will identify statistical questions, and use those questions in surveys for the purpose of analyzing data with a focus on median and range.
- CCSS.Math.Content.6.SP.A.1: Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers. For example, “How old am I?" is not a statistical question, but “How old are the students in my school?" is a statistical question because one anticipates variability in students’ ages.
- CCSS.Math.Content.6.SP.A.3: Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number.
Materials: Paper, Clipboards, Pencils
Step One: Introduction (Whole Class Discussion)
Ask students to imagine that they are being offered a chance to win a package of movie tickets, but the company offering the prize needs to know how many kids are in the family of the average student in the class in order to determine how many tickets should be included in the giveaway package.
Bring a student to the front of the class (preferably a student with one or no siblings) and ask that student how many siblings he or she has. Once the student answers the question, ask the group if it would be fair for the company to offer the amount of movie tickets based on that student’s answer. Students should react negatively to the idea, since many students might have several brothers and sisters, and would therefore not win enough tickets to take their siblings.
Lead the class in a discussion of the effectiveness of taking a single student as a sample when determining information about a group of students. Students should conclude that asking a single person a sample question does not lead to an accurate collection of data about the group of students, as in reality there is variability among student answers, and asking a question geared only toward a single student does not provide the variability present in student answers.
Step Two: Developing Statistical Questions
Students will need to understand that in order to develop an accurate collection of data, statistical questions must be used. Guide the students in rephrasing the question, “How many siblings do you have?" Students should come up with a question better suited to collection of data from a group, such as “How many siblings does the average sixth-grader have?"
Next, write five non-statistical questions on the board, asking students to rewrite them as statistical questions. Sample questions and re-writes might include the following:
- In what year were you born? (What is the birth year of the average student currently in sixth grade?)
- How many rooms are in your house? (What is the typical number of rooms in the home of each student?)
- Do you live in an apartment or a house? (Do more students live in apartments or houses?)
- What kind of pet do you have? (What is the average number of pets in student households?)
- What’s your favorite subject? (What is the preferred subject of the typical sixth grade student?)
Step Three: Class Discussion of Median and Range
Ask students to vote for a sample question to analyze. Record the answers for all students, rearranging the data visually on the board when done so that the answers are in order from lowest to highest. Demonstrate how to find the median of the data (the number directly in the center of the data) and the range of data (subtracting the lowest number from the highest).
Lead students in a discussion on the value of information such as median and range, and what each number tells them about a set of data. Students should conclude that the median gives them information on the similarities of answers in the collected data, while range gives them a picture of the variation among the answers collected.
Step Four: Application of Skill
Have students work in small groups to create a statistical question to investigate among their classmates. Allow time for students to survey their classmates to answer the statistical questions, and rotate the room to guide students as needed in finding the median and range for the data.
Let students post their data collections around the room. If there is enough time, lead a brief closing discussion on what types of questions had the smallest and largest ranges in answers, and whether the median was an accurate measure of central tendency for the questions that were asked.
Extension: Students may benefit from an additional data collection project with a focus on a set of questions to determine an overall picture of a set of data (for example, a project of student interests, including survey questions about free time after school, extracurricular activities, elective choices, plans for future areas of study, etc.).