Name Class Date. Interpreting Clusters and Outliers

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1 Name Class Date 11-2 Linear Best Fit Models Going Deeper Essential question: How can you use a trend line to make a prediction from a scatter plot? A cluster is a set of closely grouped data. Data may cluster around a point or along a line. video tutor 1 MCC8.SP.1 EXAMPLE Interpreting Clusters and Outliers 6 A scientist gathers information about the eruptions of Old Faithful, a geyser in Yellowstone National Park. She uses the data to create a scatter plot. The data shows the length of time between eruptions (interval) and how long the eruption lasts (duration). A Describe any clusters you see in the scatter plot. Duration (minutes) Interval (minutes) B What do the clusters tell you about eruptions of Old Faithful? C Describe any outliers you see in the scatter plot. REFLECT 1a. Suppose the geyser erupts for 2.2 minutes after a 75-minute interval. Would this point lie in one of the clusters? Would it be an outlier? Explain your answer. 1b. Suppose the geyser erupts after an 80-minute interval. Give a range of possible duration times for which the point on the scatter plot would not be considered an outlier. Module Lesson 2

2 2 MCC8.SP.3 EXAMPLE Finding the Equation of a Trend Line The scatter plot shows the relationship between the number of chapters and the total number of pages for several books. Draw a trend line, write an equation for the trend line, and describe the meanings of the slope and y-intercept. A Draw a trend line. It will be easier to write an equation for the line if it goes through two of the data points. (Hint: Use (5, 50) as one of the points.) Identify another point that the trend line goes through: (, ). B What type(s) of association does the scatter plot show? Pages Chapters C Do you expect the slope of the line to be positive or negative? D Find the slope of the trend line m = = = - 5 E Use the equation mx + b, the slope, and the point (5, 50). Substitute values for y, m, and x into the equation and solve for b. mx + b = + b Substitute for y, m, and x. = + b Simplify on the right side. = + b Subtract the number that is added to b from both sides. - - = b Use your slope and y-intercept values to write an equation in slope-intercept form. x + F What is the meaning of the slope in this situation? G What is the meaning of the y-intercept in this situation? Module Lesson 2

3 When you use a trend line or its equation to predict a value between data points that you already know, you interpolate the predicted value. When you make a prediction that is outside the data that you know, you extrapolate the predicted value. 3 MCC8.SP.2 EXPLORE Making Predictions Refer to the scatter plot and trend line in 2. A Use the equation of the trend line to predict how many pages would be in a book with 26 chapters. Is this prediction an example of interpolation or extrapolation? Write the equation for your trend line. Substitute the number of chapters for x. Simplify. I predict that a book with 26 chapters would have pages. B Use the equation of the trend line to predict how many pages would be in a book with 14 chapters. Is this prediction an example of interpolation or extrapolation? Write the equation for your trend line. Substitute the number of chapters for x. Simplify. I predict that a book with 14 chapters would have pages. REFLECT 3a. How well do your new points fit the original data? 3b. Do you think that extrapolation or interpolation is more accurate? Explain. Module Lesson 2

4 practice Twenty-five runners between the ages of 6 and 18 were timed in a mile run. The scatter plot shows the results. 1. In what range of running times does the data appear to cluster? 2. What running times are outliers? Time (min) Age (yr) 3. Suppose that Juan, who is 17, was timed at 9.5 minutes. Would his time be an outlier? Explain. The scatter plot shows the circumference and height of a variety of trees. 4. How would you describe the association between circumference and height that the scatter plot shows? Explain. Height (ft) Circumference (in.) 5. Using (150, 80) as one of the points, draw a trend line using a straightedge. What is the slope of the line? How did you find it? 6. What is the equation for your trend line? 7. Why might your classmates equations for trend lines vary? 8. Error Analysis A student used points (150, 80) and (50, 30) but wrote the equation 5x What mistake did the student make? Module Lesson 2

5 Name Class Date 11-2 Additional Practice Use the scatter plot for Exercises 1 6. Pay Per Hour ($) Years Worked and Hourly Wage Number of Years 1. Does the pattern of association between year and pay per hour appear to be linear or nonlinear? 2. Identify any clustering. 3. Identify any possible outliers. 4. Write an equation for the line of best fit. 5. What does the slope in the scatter plot represent? 6. What does the y-intercept in the scatter plot represent? Module Practice and Problem Solving

6 Problem Solving Use the scatter plot for Exercises Does the pattern of association between time studied and score appear to be linear or nonlinear? 2. Describe the correlation between the time studied and the scores as positive, negative, or no correlation. 3. Identify any possible outliers. Score (%) Studying and Scores Time Studied (h) Choose the letter for the best answer. Use the scatter plot for Exercises What does the point (0, 400) represent in this scatter plot? A the temperature at an elevation of 0 feet B the elevation at a temperature of 58 F C the elevation at a temperature of 0 F D the temperature at an elevation of 500 feet 5. Which best describes the correlation between the temperatures and the elevations in the scatter plot? F strong positive G weak positive H strong negative J weak negative Elevation (ft) Temperatures and Elevation Temperature ( F) 6. Which equation best represents the line of best fit? A y 16x 400 B y 15x 300 C y 15x 300 D y 16x 400 Module Practice and Problem Solving