Is “How many centimeters are in one meter?” statistical? Explain.
No; one fixed conversion, 100 cm.
Look for a collection of data and anticipated variation; identify the population and variable.
Day 121Questions That Anticipate Variability
Standards 6.SP.A.1
LEARNING TARGET
I can recognize a statistical question and the expected variability.
01 · LEARN
Build the idea
A statistical question anticipates different answers in a collection of data. Name the group, the measured attribute, and the expected variation. A question about one fixed fact is not statistical.
A survey asks “Is our school nice?” Improve it to collect numerical data with expected variation.
Example: On a 1 to 5 scale, how do students in our class rate the school library? Ratings vary among students; the numerical scale must be defined.
Look for a collection of data and anticipated variation; identify the population and variable.
02 · PRACTICE
Your turn
Work in order. Start with the foundations, then build toward explanation and application.
Is “How many pages did each student read last night?” statistical? Explain.
Is “How many centimeters are in one meter?” statistical? Explain.
Is “What are the heights of the plants in our garden?” statistical? Explain.
Identify the group, attribute, and units in: How many minutes do students in our class sleep each night?
Rewrite “How long is my pencil?” as a statistical question.
A student asks only one person’s age once. Explain why “How old is this person today?” is not statistical.
Write a statistical question about travel to school. Name the group, attribute, units, and why answers may vary.
A survey asks “Is our school nice?” Improve it to collect numerical data with expected variation.
Plan a class investigation of daily water use. Write a statistical question, identify a unit, and describe how to collect comparable data.
Critique: “A question is statistical whenever it contains numbers.” Give a counterexample and a corrected rule.
03 · CHECK
Answers and reasoning
Reveal the teacher answer key
- Yes; pages read vary across students.
Look for a collection of data and anticipated variation; identify the population and variable.
- No; one fixed conversion, 100 cm.
Look for a collection of data and anticipated variation; identify the population and variable.
- Yes; plant heights vary.
Look for a collection of data and anticipated variation; identify the population and variable.
- Group: class; attribute: sleep duration; units: minutes.
Look for a collection of data and anticipated variation; identify the population and variable.
- Example: What are the lengths in centimeters of the pencils in our classroom?
Look for a collection of data and anticipated variation; identify the population and variable.
- It seeks one fixed value, rather than anticipating variation in a data collection.
Look for a collection of data and anticipated variation; identify the population and variable.
- Example: How many minutes do students in our class take to reach school? Group: class; travel time in minutes varies with routes and travel methods.
Look for a collection of data and anticipated variation; identify the population and variable.
- Example: On a 1 to 5 scale, how do students in our class rate the school library? Ratings vary among students; the numerical scale must be defined.
Look for a collection of data and anticipated variation; identify the population and variable.
- Example: How many liters of water do students in our class drink in one day? Record each student’s total over the same 24-hour period in liters; amounts can differ.
Look for a collection of data and anticipated variation; identify the population and variable.
- Counterexample: How many sides does a triangle have? It has a fixed answer. A statistical question anticipates variability in a collection of data.
Look for a collection of data and anticipated variation; identify the population and variable.