Chapter 6: Statistics – Looking for Patterns in Data (2 Weeks)

First published in 2013 by the University of Utah with the Utah State Office of Education.
Copyright © 2013, Utah State Office of Education. This work can be shared and changed under a Creative Commons license (CC BY), which lets people reuse, change, and share it freely. This is a free educational resource.

Table of Contents

Chapter 6: Statistics – Finding Patterns Between Two Kinds of Data (2 weeks) ................ 2

• 6.0 Warm-Up Problem: Tongue Twisters ................ 7

Section 6.1: Making and Reading Scatter Plots ................ 9

• 6.1a Class Activity: Read and Understand a Scatter Plot ................ 10
• 6.1a Homework: Read and Understand a Scatter Plot ................ 16
• 6.1b Class Activity: Make and Study a Scatter Plot ................ 19
• 6.1b Homework: Make and Study a Scatter Plot ................ 21
• 6.1c Classwork: Patterns in Data ................ 23
• 6.1c Homework: Patterns in Data ................ 27
• 6.1d Check Your Understanding: Section 6.1 ................ 30

Section 6.2: Using a Straight Line to Solve Problems ................ 34

• 6.2a Classwork: Lines That Fit the Data Best ................ 35
• 6.2a Homework: Lines That Fit the Data Best ................ 39
• 6.2b Class Activity: Fit a Straight Line to Data ................ 44
• 6.2b Homework: Fit a Straight Line to Data ................ 50
• 6.2c Check Your Understanding: Section 6.2 ................ 57

Section 6.3: Making and Reading Two-Way Tables ................ 61

• 6.3a Class Activity: Build Two-Way Tables ................ 62
• 6.3a Homework: Build a Two-Way Table ................ 69
• 6.3b Class Activity: Read Two-Way Tables ................ 73
• 6.3b Homework: Read Two-Way Tables ................ 78
• 6.3c Class Activity: Do a Survey ................ 82
• 6.3d Check Your Understanding: Section 6.3 ................ 84

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What You Will Learn in This Chapter

• You will make and read scatter plots — graphs that show two kinds of data at once — to look for patterns between them. You will describe patterns like groups of points that cluster together, points that don't fit the pattern (called outliers), and whether the data goes up together, down together, or shows no clear pattern at all. You will also notice whether the pattern forms a straight line or a curved one.

• You will learn that people often use a straight line to show how two sets of numbers are connected. When a scatter plot shows a pattern that looks like a line, you can draw your own straight line to match it and check how close your line comes to the real data points.

• You will use the equation of that line to solve problems and make predictions, explaining what the slope (how steep the line is) and the starting point of the line mean in real life. For example, if a line shows that plants grow 1.5 cm taller for every extra hour of sunlight, that number tells you something meaningful about the plants.

• You will also learn that patterns can show up in a different kind of data — data sorted into categories instead of numbers. You'll organize this kind of data into a two-way table, which shows how often different combinations happen. Then you'll use the table to see if there's a connection between the two categories. For example, you might collect data from your class about whether students have a bedtime on school nights and whether they have chores at home, then check if kids with a bedtime tend to also have chores.

Important Words You'll Learn

Experiment, outcomes, all possible outcomes, random variables, number data, category data, one-variable data, two-variable data, scatter plot, connection (association), positive connection, negative connection, no connection, straight-line connection, curved connection, weak connection, strong connection, perfect connection, cluster, outlier, best-fit line, straight-line model, prediction equation, two-way table, row and column totals, how often something happens (relative frequency).

Chapter Overview

So far, you've studied data that falls neatly on a straight line. But real-world data is almost never perfect. Even so, real data often follows patterns that we can describe using math. In this chapter, you will look for patterns between two kinds of data by making and reading scatter plots. When the pattern looks like a line, you'll draw a straight line to match it and use that line's equation to solve real problems and make predictions. You will also study data sorted into categories by building and reading two-way tables.

How This Connects to What You Already Know

What you learned before: Until now, you've mostly studied one kind of data at a time. You've made graphs, described the shape of the data, and found numbers that show the middle and spread of the data. Now in 8th grade, you'll use what you know about graphing on a coordinate plane and about straight lines to study two kinds of data together and build straight-line models for data that fits a pattern.

What you'll learn later: In the future, you'll use computers to fit straight lines and other kinds of curves to data. You'll also calculate a special number that measures how strong a straight-line pattern is. You'll learn to use another kind of graph to check how well your line matches the data. And you'll keep studying two-way tables too.

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Math Practices in Action

Make sense of problems and keep trying.

Emina loves eating tomatoes from her garden in Salt Lake City. She asked her friend Renzo, "Don't you just love tomatoes?" Renzo wrinkled his nose and said, "Ew, tomatoes gross me out! When I see them at the store, I just keep walking." This made Emina think: "I don't buy tomatoes at the store either — I grow my own! My garden tomatoes taste amazing, but store tomatoes don't look appealing to me. I wonder if there's a connection between liking tomatoes and having a garden at home?"

In this kind of problem, you help Emina figure out if there really is a connection between liking tomatoes and having a garden. You collect data, organize it into a two-way table, and study what it tells you. You have to think carefully about how to organize the data and what the results mean.

Reason with numbers and ideas.

Imagine a table showing how many oil changes a car gets over two years and how much its repairs cost.

You would plot this data on a graph, putting the number of oil changes along the bottom (you'd choose your own scale). Then you'd write an equation for a line that could predict repair costs, y, based on the number of oil changes, x. You'd compare your equation with a partner's.

Then you'd use your equation to predict the repair cost for a car that gets 8 oil changes — and compare that prediction with your partner's, too.

Throughout this chapter, you'll study number data shown in tables and graphs. When the data suggests a straight-line pattern, you'll build an equation to represent it. These equations are a way of using math to describe real-world connections.

Build strong arguments and think about others' ideas.

Using a scatter plot, you might be asked to decide whether there's a connection between how many shots a player attempts and how many they make. You'd describe any patterns or trends you notice.

Throughout the chapter, you'll make scatter plots from data and study them to see if two things are connected. You'll look for trends, clusters, and outliers, and explain what they mean using the real-world situation. This means making arguments about the data and backing them up with evidence and careful thinking about what the data can — and can't — tell you.

Use math to model real situations.

In one activity, students say a tongue twister one at a time. In the first round, only the first student says it. In the second round, the first two students say it together. Each round, one more student joins in, and the total time is recorded.

Some tongue twisters used are:

• A. "Work will win when wishy-washy wishing won't."
• B. "Three witches wished three wishes, but which witch wished which wish."
• C. "Peter Piper picked a peck of pickled peppers."
• D. "Picky peopl..." (passage continues)