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Posing Statistical Questions




 

Video Solutions to help grade 6 students learn how to distinguish between statistical questions and those that are not statistical.

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Lesson Plans and Worksheets for Grade 6

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Common Core For Grade 6

New York State Common Core Math Module 6, Grade 6, Lesson 1



Lesson 1 Student Outcomes

• Students distinguish between statistical questions and those that are not statistical.
• Students formulate a statistical question and explain what data could be collected to answer the question.
• Students distinguish between categorical data and numerical data.

Lesson 1 Summary

A statistical question is one that can be answered by collecting data that vary (i.e., not all of the data values are the same).
There are two types of data: numerical and categorical. In a numerical data set, every value in the set is a number. Categorical data sets can take on non-numerical values, such as names of colors, labels, etc. (e.g., “large,” “medium,” or “small”).

Lesson 1 Classwork

Statistics is about using data to answer questions. In this module, the following four steps will summarize your work with data:
Step 1: Pose a question that can be answered by data.
Step 2: Determine a plan to collect the data.
Step 3: Summarize the data with graphs and numerical summaries.
Step 4: Answer the question posed in Step 1 using the data and summaries.
You will be guided through this process as you study these lessons. This first lesson is about the first step – what is a statistical question, and what does it mean that a question can be answered by data?

Example 1: What is a Statistical Question?
Jerome, a 6th grader at Roosevelt Middle School, is a huge baseball fan. He loves to collect baseball cards. He has cards of current players and of players from past baseball seasons. With his teacher’s permission, Jerome brought his baseball card collection to school. Each card has a picture of a current or past major league baseball player, along with information about the player. When he placed his cards out for the other students to see, they asked Jerome all sorts of questions about his cards. Some asked:
• How many cards does Jerome have altogether?
• What is the typical cost of a card in Jerome’s collection?
• Where did Jerome get the cards?

Exercises 1–5
1. For each of the following, determine whether or not the question is a statistical question. Give a reason for your answer.
a. Who is my favorite movie star?
b. What are the favorite colors of 6th graders in my school?
c. How many years have students in my school’s band or orchestra played an instrument?
d. What is the favorite subject of 6th graders at my school?
e. How many brothers and sisters does my best friend have?

2. Explain why each of the following questions is not a statistical question.
a. How old am I?
b. What’s my favorite color?
c. How old is the principal at our school?

3. Ronnie, a 6th grader, wanted to find out if he lived the farthest from school. Write a statistical question that would help Ronnie find the answer.

4. Write a statistical question that can be answered by collecting data from students in your class.

5. Change the following question to make it a statistical question: “How old is my math teacher?”




Example 2: Types of Data
We use two types of data to answer statistical questions: numerical data and categorical data. If we recorded the age of 25 baseball cards, we would have numerical data. Each value in a numerical data set is a number. If we recorded the team of the featured player for 25 baseball cards, you would have categorical data. Although you still have 25 data values, the data values are not numbers. They would be team names, which you can think of as categories.

Exercises 6–7
6. Identify each of the following data sets as categorical (C) or numerical (N).
a. Heights of 6th graders
b. Favorite flavor of ice cream for each of 6th graders
c. Hours of sleep on a school night for 6th graders
d. Type of beverage drank at lunch for each of 6th graders
e. Eye color for each of 6th graders
f. Number of pencils in each desk of 6th graders

7. For each of the following statistical questions, students asked Jerome to identify whether the data are numerical or categorical. Explain your answer, and list four possible data values.
a. How old are the cards in the collection?
b. How much did the cards in the collection cost?
c. Where did you get the cards?


 

Rotate to landscape screen format on a mobile phone or small tablet to use the Mathway widget, a free math problem solver that answers your questions with step-by-step explanations.


You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.



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