1-8 Scatter Plots. Learn to display and analyze data in scatter plots. Course 2

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1 Learn to display and analyze data in scatter plots.

2 Vocabulary scatter plot positive correlation negative correlation no correlation

3 To find out if two sets of data may be related, you can make a scatter plot of the data values in each set. A scatter plot has two number lines, called axes one for each set of data values. Each point on the scatter plot represents a pair of data values. These points may appear to be scattered or may cluster in the shape of a line or a curve.

4 Additional Example 1: Making a Scatter Plot Use the data to make a scatter plot. Describe the relationship between the data sets Number of Endangered Species Type U.S. Only Rest of World Mammals Birds Reptiles Amphibians 10 8 Fishes Clams Step 1: Determine the scale and interval for each axis. Place the number of animals endangered in the U.S. on the horizontal axis and the number of animals endangered in the rest of the world on the vertical axis.

5 Additional Example 1 Continued Number of Endangered Species Type U.S. Only Rest of World Mammals Birds Reptiles Amphibians 10 8 Fishes Clams Step 2: Plot a point for each pair of values.

6 Rest of World 1-8 Scatter Plots Additional Example 1 Continued Use the data to make a scatter plot. Describe the relationship between the data sets. Number of Endangered Species U.S. Number of Endangered Species Type U.S. Only Rest of World Mammals Birds Reptiles Amphibians 10 8 Fishes Clams 61 2 Step 3: Label the axes and give the graph a title.

7 Rest of World 1-8 Scatter Plots Additional Example 1 Continued Use the data to make a scatter plot. Describe the relationship between the data sets. Number of Endangered Species U.S. Number of Endangered Species Type U.S. Only Rest of World Mammals Birds Reptiles Amphibians 10 8 Fishes Clams 61 2 There appears to be no relationship between the data sets.

8 Try This: Example 1 Use the data to make a scatter plot. Describe the relationship between the data sets. 10,000 8,000 6,000 2, Year Number of farm workers in thousands , , , , , ,864 Step 1: Determine the scale and interval for each axis. Place the year on the horizontal axis and the cost on the vertical axis.

9 Try This: Example 1 Continued 10,000 8,000 6,000 2, Year Number of farm workers in thousands , , , , , ,864 Step 2: Plot a point from each pair of values.

10 Number (in thousands) 1-8 Scatter Plots 10,000 8,000 6,000 2,000 Try This: Example 1 Continued Number of Farm Workers Year Year , , , , , ,864 Step 3: Label the axes and give the graph a title. Number of farm workers in thousands

11 Number (in thousands) 1-8 Scatter Plots 10,000 8,000 6,000 2,000 Try This: Example 1 Continued Number of Farm Workers Year Year Number of farm workers in thousands , , , , , ,864 The number of farm workers decreased from 1940 to 1970.

12 There are three ways to describe data displayed in a scatter plot. Positive Correlation Negative Correlation No Correlation The values in both data sets increase at the same time. The values in one data set increase as the values in the other set decrease. The values in both data sets show no pattern.

13 Additional Example 2A: Determining Relationships Between Two Variables Write positive correlation, negative correlation, or no correlation to describe each relationship. Population by County Population (thousands) Area (square miles) The graph shows that as area increases, population increases. So the graph shows a positive correlation between the data sets.

14 Additional Example 2B: Determining Relationships Between Two Variables Write positive correlation, negative correlation, or no correlation to describe each relationship. Sales (millions) Record Sales Year The graph shows that as the year increases, sales decrease. So the graph shows a negative correlation between the data sets.

15 Additional Example 2C: Determining Relationships Between Two Variables Write positive correlation, negative correlation, or no correlation to describe each relationship. height and number of vacation days The number of vacation days is not related to height. So there would not be any correlation between these two variables.

16 Try This: Example 2A Write positive correlation, negative correlation, or no correlation to describe each relationship. Number of Tornados Tornado Frequency Year The graph shows that as the year increases, number of tornados increases. So the graph shows a positive correlation between the data sets.

17 Try This: Example 2B Write positive correlation, negative correlation, or no correlation to describe each relationship. Frequency (vps) Guitar String Frequency Length of string (cm) The graph shows that as the length of string increases, frequency decreases. So the graph shows a negative correlation between the data sets. vps = vibrations per second

18 Try This: Example 2C Write positive correlation, negative correlation, or no correlation to describe each relationship. eye color and age There would not be any correlation between these two variables.

19 1-9 Misleading Graphs Learn to identify and analyze misleading graphs.

20 1-9 Misleading Graphs A data display that distorts information in order to persuade can be misleading. An axis in a graph can be broken to make the graph easier to read. However, a broken axis can also be misleading. In the graph at right, the cost per minute for service with Company B looks like it is twice as much as the cost for service with Company A. In fact, the difference is only $0.10 per minute.

21 1-9 Misleading Graphs ( F) Temperature ( F) Additional Example 1 Both line graphs show the high temperature Monday through Friday. Which graph could be misleading? Why? Temperature High Temperature M Tu W Th F Day High Temperature The graph on the right could be misleading. The vertical axis is broken, so differences in temperature appear greater M Tu W Th F Day

22 1-9 Misleading Graphs Price per meal Try This: Example 1 Which graph could be misleading? Why? Average Restaurant Meal Price Price per meal25 Graph A Graph B 0 Gino s Village Grill Pasta City City Diner 10 Gino s Village Grill Pasta City Graph B could be misleading. The vertical axis does not begin with zero, so differences in scales appear greater. City Diner

23 1-9 Misleading Graphs Additional Example 2A: Analyzing Misleading Graphs Explain how you could redraw the graph so it would not be misleading. Draw the entire vertical scale on the graph.

24 1-9 Misleading Graphs Additional Example 2B: Analyzing Misleading Graphs Explain how you could redraw the graph so it would not be misleading. Draw the vertical scale with equal spacing between marks so that the distance between 0 and 18,000 equals the distance between 18,000 and 36,000.

25 1-9 Misleading Graphs Try This: Example 2A Explain how you could redraw the graph so it would not be misleading. Draw the entire vertical scale on the graph. The vertical axis is broken, so differences in fare appear greater Taxicab Fares Mon Tue Wed Thu Fri

26 1-9 Misleading Graphs Ounces of Water Try This: Example 2B Explain how you could redraw the graph so it would not be misleading. Draw the entire vertical scale on the graph. The vertical axis does not start at zero so differences in water consumed seem greater Water Consumed Mark Frank Mila Yvonne

27 Lesson Quiz: Part 1 1. The table shows the daily attendance at the beach. Use the data to make a scatter plot of the data and describe the relationship between the data sets. Temperature Attendance Attendance Beach Attendance Temperature The graph shows a positive correlation.

28 Lesson Quiz: Part 2 2. Write positive, negative, or no correlation to describe the relationship shown. Movie Attendance 1500 Attendance Age negative correlation

29 1-9 Misleading Graphs Lesson Quiz: Part 1 Explain why each graph could be misleading and why. The vertical scale on the graph is not small enough to show the changes, so it appears to be unchanging and flat.

30 1-9 Misleading Graphs Lesson Quiz: Part 2 Explain why each graph could be misleading and why. The scale does not start at 0, so it emphasizes the differences in bar heights more.

31 Homework 1-8 and 1-9 Worksheet Study for 1-1 to 1-9 test Thursday

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