Page 198 #1-3 ANSWERS. Pre-Algebra 4-6 Misleading Graphs and Statistics Student Learning Goal Chart Lesson Reflection for Chapter 4 Section 6

Page 198 #1-3 ANSWERS

Pre-Algebra

4-6 Misleading Graphs and Statistics

Student Learning Goal

ChartLesson Reflection for

Chapter 4 Section 6

Pre-Algebra


Pre-Algebra Learning GoalStudents will

understand collecting, displaying, &

analyzing data.

Pre-Algebra


Students will understand collecting, displaying & analyzing data by being able to do the following:

• Learn to identify populations & recognize biased samples (4-1)• Learn to organize data in tables and stem-and-leaf plots (4-2)• Learn to find Euler circuits (14-6)• Learn to find and use Hamiltonian circuits (14-7)• Learn to find appropriate measures of central tendency (4-3)• Learn to find measures of variability (4-4)• Learn to display data in bar graphs, histograms, and line graphs (4-5)• Learn to recognize misleading graphs and statistics (4-6)

Pre-Algebra


Today’s Learning Goal Assignment

Learn to recognize misleading graphs and statistics.

Pre-Algebra


Pre-Algebra HW

Page 202

#1-4

Pre-Algebra

4-6 Misleading Graphs and Statistics4-6 Misleading Graphs and Statistics

Pre-Algebra

Warm Up

Problem of the Day

Lesson Presentation

Pre-Algebra


Warm Up

1. How many students say oranges are their favorite?

2. What is the least popular fruit?

3. How many students answered the survey?

40

kiwi

90

Pre-Algebra


Use the graph for problems 1-3

Pre-Algebra


Problem of the Day

Create a data set with five values that will have a mean of 20, a median of 18, and a mode of 15.

Possible answer: 15, 15, 18, 19, 33

Pre-Algebra


Today’s Learning Goal Assignment

Learn to recognize misleading graphs and statistics.

Pre-Algebra


For example, art is often used to make a graph more interesting, but it can distort the relationships in the data.

Graphs and statistics are often used to persuade. Advertisers and others may accidentally or intentionally present information in a misleading way.

Pre-Algebra


Additional Example 1A: Identifying Misleading Graphs

Explain why each graph is misleading.

A. The graph suggests that the stock will continue to increase through 2020, but there’s no way to foresee the future.

Pre-Algebra


Try This: Example 1A

Explain why each graph is misleading.A.

0

10

20

30

40

50

60

1 2 3 4 5* 6** projected

% of Return on Investment

The graph suggests that the rate of investment return will continue to increase, but there are no guarantees

Pre-Algebra


Additional Example 1B: Identifying Misleading Graphs


Because the scale leaves out 0 to 100, the bar heights make it appear that the sixth grade sold about three times as many tickets as either of the other two grades. In fact, the sixth grade sold only about 20% more.

B.

Pre-Algebra


Try This: Example 1B


B.

140

142

144

146

148

150Preferred Juice Flavors

Grape Cherry Apple

The graph appears to indicate that significantly more people prefer grape drink over the others when in fact there is a small margin of difference. (0 to 140 is not graphed)

Pre-Algebra


Additional Example 1C: Identifying Misleading Graphs


The scale is so compressed that it’s hard to see any difference among the brands.

C.

Pre-Algebra


Try This: Example 1C


C.

0

20

40

60

80

100

120

Brand X Brand Y Brand Z

Drink Sales This graph is too compressed to see much difference between the brands indicating that they are fairly equal.

No data from 50 to 120

Pre-Algebra


Additional Example 2: Identifying Misleading Graphs

Explain why each statistic is misleading.

A. Sam scored 43 goals for his soccer team during the season, and Jacob scored only 2.

Although Jacob scored only 2 goals, he may have played most of his time on defense.

B. Four out of five dentists surveyed preferred UltraClean toothpaste.

This statement does not give the sample size or state what UltraClean toothpaste was compared with.

Pre-Algebra



Try This: Example 2A & 2B

A. Four out of five breeders recommend Pet Blend dog food for a healthier coat.

This statement does not give the sample size or state what Science Blend dog food was compared with.

B. Fruity Squares makes the cereal 100% more fun.

You cannot measure how much fun Fruity Squares makes the cereal.

Pre-Algebra


Additional Example 2 Continued


C. Shopping at Save-a-Lot can save you up to $100 a month!

The words save up to $100 mean that the maximum you can save is $100, but there is no guarantee that you will save that amount.

Pre-Algebra



C. The total revenue for bathing suits sold in May at Worthman’s Florida stores is 250,000. The total revenue for bathing suits sold in May at Worthman’s North Dakota stores is 10,000.

The states have different populations and climates.

Try This: Example 2C

Pre-Algebra


Lesson Quiz: Part 1

Possible answer: The size of the trucks is larger than the size of the cars, so it looks like there are as many trucks as cars, although there are 6 cars and 4 trucks.

1.

Explain why each graph or statistic is misleading

Pre-Algebra


Lesson Quiz: Part 2

2. A budget area of a used-car lot has five cars on it, with prices of $4200, $4700, $4900, $5200, and $900 (a wrecked one). The car ad in the local paper reads “Average priced car on budget lot is $3980.”

The wrecked car’s price brings the average down. Without using the price of the wrecked car, the average price would be $4750.

Explain why each graph or statistic is misleading

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Page 198 #1-3 ANSWERS. Pre-Algebra 4-6 Misleading Graphs and Statistics Student Learning Goal Chart Lesson Reflection for Chapter 4 Section 6