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Understanding Scatter Plots and Correlations in Data Analysis

This chapter explores scatter plots, a graphical representation that illustrates possible relationships between two data sets. We begin with a problem involving a savings account deposit and its percentage increase, leading to an analysis of key concepts, including scatter plots, correlations, and trend lines. You'll learn how to create scatter plots, interpret correlations, and recognize how data sets interact. Examples range from measuring cookies in a jar to analyzing football scores, guiding you through practical applications of these statistical tools.

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Understanding Scatter Plots and Correlations in Data Analysis

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  1. Chapter 3 3-5 Scatter plots

  2. SAT Problem of the day • Nicoletta deposits $150 in her savings account. If this deposit represents a 12 percent increase in her savings, then how much does her savings account contain after the deposit? • A)$1,100 • B)$1,250 • C)$1400 • D)$1680 • E)1,800

  3. Solution to the problem of the day • Right Answer: C

  4. Objectives • Create and interpret scatter plots. • Use trend lines to make predictions.

  5. Scatter plot • What is a scatter plot? • A scatter plot is a graph with points plotted to show a possible relationship between two sets of data. A scatter plot is an effective way to display some types of data.

  6. Example#1 • The table shows the number of cookies in a jar from the time since they were baked. Graph a scatter plot using the given data.

  7. Example#2 • The table shows the number of points scored by a high school football team in the first four games of a season. Graph a scatter plot using the given data. • Game Score • 1 6 • 2 21 • 3 46 • 4 34

  8. Student guided practice • Do problem 4 in your book page 200

  9. Correlation • What is a correlation? • A correlation describes a relationship between two data sets. A graph may show the correlation between data. The correlation can help you analyze trends and make predictions. There are three types of correlations between data.

  10. Types of correlation

  11. Example#3 • Describe the correlation illustrated by the scatter plot. As the average daily temperature increased, the number of visitors increased. There is a positive correlation between the two data sets

  12. Example#4 • Describe the correlation illustrated by the scatter plot. There is a positive correlation between the two data sets.

  13. Student guided practice • Do problems 5 and 6 in your book page 200

  14. Example #5 • Identify the correlation you would expect to see between the pair of data sets. Explain. • the average temperature in a city and the number of speeding tickets given in the city • You would expect to see no correlation. The number of speeding tickets has nothing to do with the temperature.

  15. Example#6 • Identify the correlation you would expect to see between the pair of data sets. Explain. • the number of people in an audience and ticket sales • You would expect to see a positive correlation. As ticket sales increase, the number of people in the audience increases.

  16. Example#7 • Identify the correlation you would expect to see between the pair of data sets. Explain. • a runner’s time and the distance to the finish line • You would expect to see a negative correlation. As time increases, the distance to the finish line decreases.

  17. Student guided practice • Do problems 7-9 in your book page 200

  18. Matching Scatter plots • Choose the scatter plot that best represents the relationship between the age of a car and the amount of money spent each year on repairs. Explain. • Graph A Graph B Graph C

  19. solution • Graph B

  20. Example#8 • Choose the scatter plot that best represents the relationship between the number of minutes since a pie has been taken out of the oven and the temperature of the pie. Explain. • Graph A Graph B Graph C

  21. Solution • Graph A Graph B shows the pie cooling while it is in the oven, so it is incorrect. Graph C shows the temperature of the pie increasing, so it is incorrect. Graph A is the correct answer.

  22. Student guided practice • Do problems 10-11

  23. What is the trend line? • You can graph a function on a scatter plot to help show a relationship in the data. Sometimes the function is a straight line. This line, called a trend line, helps show the correlation between data sets more clearly. It can also be helpful when making predictions based on the data.

  24. Example • The scatter plot shows a relationship between the total amount of money collected at the concession stand and the total number of tickets sold at a movie theater. Based on this relationship, predict how much money will be collected at the concession stand when 150 tickets have been sold.

  25. solution Based on the data, $750 is a reasonable prediction of how much money will be collected when 150 tickets have been sold.

  26. Homework !! • Do problems 14-20 in your book page 201

  27. Quiz #3 • 1. Write a possible situation for the given graph. • 2. Express the relation {(–2, 5), (–1, 4), (1, 3), (2, 4)} as a table, as a graph, and as a mapping diagram.

  28. Quiz#3 • 3. Give the domain and range of the relation. Tell whether the relation is a function. Explain.

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