Lesson 8.1 · Statistics
Statistical questions
Statistics is the math of answering questions with data. But not every question needs data. Before you collect anything, you need to know whether your question is a statistical question: one where you expect the answers to vary.
Questions with one answer vs. many answers
Compare these two questions:
- "How tall is Ms. Rivera?"
- "How tall are the students in Ms. Rivera's class?"
The first question has one answer. You measure one person once and you're done. The second question has many answers, because students are different heights. To answer it, you have to collect many measurements and then describe them as a group.
That difference is the whole idea. Differences in the answers are called variability.
Definition
Statistical question
A statistical question is a question that you expect to have answers that vary. You answer it by collecting data and describing the whole set of data, not just one value.
Here are more pairs. In each pair, the second question is statistical.
| Not statistical | Statistical |
|---|---|
| How many pets does Jordan have? | How many pets do the students at my school have? |
| What time does the bus arrive today? | What time does the bus arrive each day this month? |
| How many pages are in this book? | How many pages are in the books in the school library? |
A good test is to ask yourself: "If I asked this question many times, or of many people, would I get different answers?" If yes, it's statistical.
Worked example: Sorting questions
Decide whether each question is statistical.
- How many hours of sleep did sixth graders at Lincoln Middle School get last night?
- How many days are in April?
- How much does a gallon of milk cost at different stores in town?
- What is the temperature in my backyard right now?
Solutions.
- Statistical. Different students sleep different amounts, so the answers vary.
- Not statistical. April always has 30 days. There is one answer.
- Statistical. Prices change from store to store.
- Not statistical. You read one thermometer once and get one number.
Turning a question into a statistical one
You can often turn a one-answer question into a statistical question by asking it about a group or over time.
Worked example: Rewriting a question
"How many minutes did Priya spend on homework last night?" has one answer. Rewrite it as a statistical question.
Solution. Ask about many people or many nights:
- "How many minutes did the students in Priya's class spend on homework last night?"
- "How many minutes did Priya spend on homework each night last month?"
Both of these will give you a set of different numbers.
Common mistake
A question isn't statistical just because it has a number in the answer or mentions a group. "How many students are in our class?" is about a group, but it has one answer (say, 27). Ask yourself whether the answers will vary, not whether a group is mentioned.
Describing a set of data
When you answer a statistical question, you end up with a list of values called a data set. The way the values are spread out is called the distribution of the data. In this unit, you'll learn to describe a distribution in three ways:
Three ways to describe data
- Center: What is a typical value? (You'll learn the mean and median.)
- Spread: How much do the values vary? (You'll learn the range, interquartile range and mean absolute deviation.)
- Shape: What does the data look like on a graph? Is it bunched up, lopsided, or does it have gaps?
Worked example: Planning a data collection
Leo wants to know how far students in his grade live from school.
- Write his statistical question.
- What kind of data will he collect?
- If he asks 60 students, how many data values will he have?
Solutions.
- "How far do the sixth graders at my school live from school?"
- Distances, such as numbers of miles. This is numerical data (numbers you can measure or count).
- One value per student, so 60 data values.
Tip
Statistical questions usually talk about "the students," "each day," "different stores," or "the players." Words that point to many people, many times or many things are a clue, but always check that the answers really vary.
Practice
Which question is a statistical question?
Which question is not a statistical question?
Amara asks each of the 32 students in her grade, "How many books did you read this summer?" How many data values will she collect?
Enter a number. Fractions like 3/4 and sqrt(2) are OK.
"How long is the Mississippi River?" has one answer. Which question turns it into a statistical question?
Mateo records the high temperature in his town every day for a month. Which statistical question is he most likely trying to answer?
Which question would give data that describes spread, meaning how much the values vary?