11-1 Scatter Plots Going Deeper

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1 Name Class Date 11-1 Scatter Plots Going Deeper Essential question: How can you construct and interpret scatter plots? A set of bivariate data involves two variables. Bivariate data are used to explore the relationship between two variables. You can graph bivariate data on a scatter plot. A scatter plot is a graph with points plotted to show the relationship between two sets of data. video tutor 1 EXPLORE Making a Scatter Plot Hours Spent Test Grade Studying The final question on a math test reads, How many hours did you spend studying for this test? The teacher 0 7 records the number of hours each student studied and the grade the student received on the test A Make a prediction about the relationship between the number of hours spent studying and test grades. B Make a scatter plot. Graph hours spent studying as the independent variable and test grade as the dependent variable. REFLECT MCC8.SP.1 1a. What trend do you see in the data? Test Grade Hours Spent Studying 1b. Do you think that studying for hours would greatly increase a student s grade? 1c. Why might a student who studied fewer hours make a higher score? Module 11 1 Lesson 1

2 Association tells you how sets of data are related. A positive association means that both data sets increase together. A negative association means that as one data set increases, the other decreases. No association means that changes in one data set do not affect the other data set. y y y x 0 Positive Association 0 Negative Association x 0 No Association x When data shows a positive or negative association and falls along a line, there is a linear association. When data shows a positive or negative relationship, but does not fall along a line, there is a nonlinear association. MCC8.SP.1 EXPLORE Determining Association Susan surveyed 0 people about the price of a cleaning product she developed. She asked each person whether they would buy the cleaner at different prices. A person may answer yes or no to more than one price. Susan s results are shown in the table. Price ($) Buyers A Make a scatter plot of the data. Buyers Price B Describe the type(s) of association you see between price and number of people who would buy at that price. Explain. Module 11 Lesson 1

3 When a scatter plot shows a linear association, you can use a line to model the relationship between the variables. A trend line is a straight line that comes closest to the points on a scatter plot. When drawing a trend line, ignore any outliers. An outlier is a data point that is very different from the rest of the data in the set. 3 MCC8.SP. EXPLORE Drawing a Trend Line Joyce is training for a K race. For some of her training runs, she records the distance she ran and how many minutes she ran. A Make a scatter plot of Joyce s running data. Time (min) Distance (mi) Time (min) Distance (mi) B To draw a trend line, use a straight edge to draw a line that has about the same number of points above and below it. Ignore any outliers. C Use your trend line to predict how long it would take Joyce to run 4. miles. REFLECT 3a. How well does your trend line fit the data? 3b. Do you think you can use a scatter plot that shows no association to make a prediction? Explain your answer. Module 11 3 Lesson 1

4 practice The table shows softball game results. Hits Runs Use the data table to make a scatter plot.. Draw a trend line using a straightedge. 3. Describe the trend your line shows. Is it positive or negative, or is there no trend? How do you know? Runs Hits 4. What does your scatter plot show about the relationship between hits and runs scored for this team?. Predict how many runs the softball team would score if its players got 9 hits. What if they got 3 hits? The table shows age and sleep times for some people. Age (yr) Sleep (h) Use the data in the table to make a scatter plot. 7. Draw a trend line using a straightedge. 8. What does your scatter plot show about the relationship between age and hours of sleep for this group of people? Sleep (h) Age (yr) 9. Predict how many hours of sleep an 18-year old might get nightly. How many hours of sleep might a 4-year old get? Module 11 4 Lesson 1

5 Name Class Date 11-1 Additional Practice 1. Use the given data to make a scatter plot, and describe the correlation. Tall Buildings in U.S. Cities Building City Stories Height (meters) Sears Tower Chicago 1 44 Empire State Building New York 381 Bank of America Plaza Atlanta 31 Library Tower Los Angeles 7 3 Key Tower Cleveland 7 90 Columbia Seafirst Center Seattle NationsBank Plaza Dallas 7 81 NationsBank Corporate Center Charlotte Make a scatter plot of the data, and draw a line of best fit. Then use the data to predict the percentage of American homeowners in 19. Percent of Americans Owning Homes Year Percent.0% 61.9% 6.9% 64.4% 64.% Module 11 Practice and Problem Solving

6 Problem Solving Use the data given at the right. 1. Make a scatter plot of the data. Percent of Americans Who Have Completed High School Year Percent Does the data show a positive, negative or no correlation? Choose the letter for the best answer. 4. Which data sets have a positive correlation? A The length of the lines at amusement park rides and the number of rides you can ride in a day B The temperature on a summer day and the number of visitors at a swimming pool C The square miles of a state and the population of the state in the 000 census D The length of time spent studying and doing homework and the length of time spent doing other activities 3. Use the scatter plot to predict the percent of Americans who will complete high school in 0.. Which data sets have a negative correlation? F The number of visitors at an amusement park and the length of the lines for the rides G The amount of speed over the speed limit when you get a speeding ticket and the amount of the fine for speeding H The temperature and the number of people wearing coats J The distance you live from school and the amount of time it takes to get to school Module 11 6 Practice and Problem Solving