9. Scatter Plots How can ou construct and interpret a scatter plot? ACTIVITY: Constructing a Scatter Plot Work with a partner. The weights (in ounces) and circumferences C (in inches) of several sports balls are shown. Basketball Soccer Baseball Tennis oz 9 in. 2 oz 3 in. Golf 2 oz 8 in..6 oz.3 in. 6 oz 28 in. Water Polo Softball Racquetball.4 oz 7 in. 7 oz 2 in. oz 27 in. Data Analsis In this lesson, ou will construct and interpret scatter plots. describe patterns in scatter plots. Learning Standard 8.SP. b. Write the weight and circumference C of each ball as an ordered pair. Then plot the ordered pairs in the coordinate plane. c. Describe the relationship between weight and circumference. Are an of the points close together? d. In general, do ou think ou can describe this relationship as positive or negative? linear or nonlinear? Eplain. oz 26 in. C Circumference (inches) a. Choose a scale for the horizontal ais and the vertical ais of the coordinate plane shown. COMMON CORE Volleball V Weight (ounces) e. A bowling ball has a weight of 22 ounces and a circumference of 27 inches. Describe the location of the ordered pair that represents this data point in the coordinate plane. How does this point compare to the others? Eplain our reasoning. 372 Chapter 9 Data Analsis and Displas
2 ACTIVITY: Constructing a Scatter Plot Math Practice Recognize Usefulness of Tools How do ou know when a scatter plot is a useful tool for making a prediction? Work with a partner. The table shows the number of absences and the final grade for each student in a sample. a. Write the ordered pairs from the table. Then plot them in a coordinate plane. b. Describe the relationship between absences and final grade. How is this relationship similar to the relationship between weight and circumference in Activit? How is it different? c. MODELING A student has been absent 6 das. Use the data to predict the student s final grade. Eplain how ou found our answer. Absences Final Grade 9 3 88 2 9 83 7 79 9 7 4 8 94 6 8 7 3 ACTIVITY: Identifing Scatter Plots Work with a partner. Match the data sets with the most appropriate scatter plot. Eplain our reasoning. a. month of birth and birth weight for infants at a da care b. quiz score and test score of each student in a class c. age and value of laptop computers i. ii. iii. 4. How would ou define the term scatter plot?. IN YOUR OWN WORDS How can ou construct and interpret a scatter plot? Use what ou learned about scatter plots to complete Eercise 7 on page 376. Section 9. Scatter Plots 373
9. Lesson Lesson Tutorials Ke Vocabular scatter plot, p. 374 Scatter Plot A scatter plot is a graph that shows the relationship between two data sets. The two sets of data are graphed as ordered pairs in a coordinate plane. EXAMPLE Interpreting a Scatter Plot Calories Restaurant Sandwiches 8 7 7 6 6 4 4 3 3 2 2 3 3 4 4 Fat (grams) The scatter plot at the left shows the amounts of fat (in grams) and the numbers of calories in 2 restaurant sandwiches. a. How man calories are in the sandwich that contains 7 grams of fat? Restaurant Sandwiches Draw a horizontal line from the point that has 8 an -value of 7. It 7 crosses the -ais at 4. So, the sandwich has 4 calories. b. How man grams of fat are in the sandwich that contains 6 calories? Draw a vertical line from the point that has a -value of 6. It crosses the -ais at 3. Calories 7 6 6 4 4 3 3 2 2 3 3 4 4 Fat (grams) So, the sandwich has 3 grams of fat. c. What tends to happen to the number of calories as the number of grams of fat increases? Looking at the graph, the plotted points go up from left to right. So, as the number of grams of fat increases, the number of calories increases. Eercises 8 and 9. WHAT IF? A sandwich has 6 calories. Based on the scatter plot in Eample, how man grams of fat would ou epect the sandwich to have? Eplain our reasoning. 374 Chapter 9 Data Analsis and Displas
A scatter plot can show that a relationship eists between two data sets. Positive Linear Negative Linear Nonlinear Relationship Relationship Relationship No Relationship O O O O The points lie close to a line. As increases, increases. The points lie close to a line. As increases, decreases. The points lie in the shape of a curve. The points show no pattern. EXAMPLE 2 Identifing Relationships Describe the relationship between the data. Identif an outliers, gaps, or clusters. a. television size and price b. age and number of pets owned Television Size and Price Age and Pets Owned Price (dollars) 3 3 2 2 2 3 4 6 7 Number of pets owned 7 6 4 3 2 2 3 4 6 7 Television size (inches) Person s age (ears) The points appear to lie close to a line. As increases, increases. So, the scatter plot shows a positive linear relationship. There is an outlier at (7, 22), a cluster of data under $, and a gap in the data from $ to $. The points show no pattern. So, the scatter plot shows no relationship. There are no obvious outliers, gaps, or clusters in the data. Eercises 2 2. Make a scatter plot of the data and describe the relationship between the data. Identif an outliers, gaps, or clusters. Stud Time (min), 3 2 6 9 4 3 7 2 8 Test Score, 8 74 92 97 8 62 83 9 7 9 Section 9. Scatter Plots 37
9. Eercises Help with Homework. VOCABULARY What tpe of data do ou need to make a scatter plot? Eplain. 2. REASONING How can ou identif an outlier in a scatter plot? LOGIC Describe the relationship ou would epect between the data. Eplain. 3. shoe size of a student and the student s IQ 4. time since a train s departure and the distance to its destination. height of a bouncing ball and the time since it was dropped 6. number of toppings on a pizza and the price of the pizza 9+(-6)=3 3+(-3)= 4+(-9)= 9+(-)= 7. JEANS The table shows the average price (in dollars) of jeans sold at different stores and the number of pairs of jeans sold at each store in one month. Average Price 22 4 28 3 46 Number Sold 2 94 34 8 a. Write the ordered pairs from the table and plot them in a coordinate plane. b. Describe the relationship between the two data sets. 8. SUVS The scatter plot shows the numbers of sport utilit vehicles sold in a cit from 29 to 24. a. In what ear were SUVs sold? b. About how man SUVs were sold in 23? c. Describe the relationship shown b the data. Number sold 2 8 6 4 2 SUV Sales 29 2 23 Year Earnings of a Food Server Earnings (dollars) 8 7 6 4 3 2 2 3 4 6 Hours worked 9. EARNINGS The scatter plot shows the total earnings (wages and tips) of a food server during one da. a. About how man hours must the server work to earn $7? b. About how much did the server earn for hours of work? c. Describe the relationship shown b the data. 376 Chapter 9 Data Analsis and Displas
2 Describe the relationship between the data. Identif an outliers, gaps, or clusters... 2. 4 4 3 4 4 3 3 3 2 2 2 2 2 2 3 3 4 2 2 3 3 4 4 4 3 3 2 2 2 2 3 3 4 3. HONEY The table shows the average price per pound for hone in the United States from 29 to 22. What tpe of relationship do the data show? Year, 29 2 2 22 Average Price per Pound, $4.6 $4.8 $. $.3 4. TEST SCORES The scatter plot shows the numbers of minutes spent studing and the test scores for a science class. (a) What tpe of relationship do the data show? (b) Interpret the relationship.. OPEN-ENDED Describe a set of real-life data that has a negative linear relationship. Stud Time and Test Scores Test scores 9 8 7 3 4 6 7 9 Stud time (minutes) 6. PROBLEM SOLVING The table shows the memor capacities (in gigabtes) and prices (in dollars) of 7-inch tablet computers at a store. (a) Make a scatter plot of the data. Then describe the relationship between the data. (b) Identif an outliers, gaps, or clusters. Eplain wh ou think the eist. Memor (GB), 8 6 4 32 4 6 4 8 6 8 6 8 Price (dollars), 2 23 2 2 2 9 6 8 22 7. Sales of sunglasses and beach towels at a store show a positive linear relationship in the summer. Does this mean that the sales of one item cause the sales of the other item to increase? Eplain. Use a graph to solve the equation. Check our solution. (Section.4) 8. = 2 + 6 9. 7 + 3 = 9 3 2. 2 3 = 3 4 2. MULTIPLE CHOICE When graphing a proportional relationship represented b = m, which point is not on the graph? (Section 4.3) A (, ) B (, m) C (, m) D (2, 2m) Section 9. Scatter Plots 377