Lesson 6.2.2

1. Shapes of Scatterplots Lesson 6.2.2

2. Lesson 6.2.2 Shapes of Scatterplots California Standard: Statistics, Data Analysis, and Probability 1.2 Represent two numerical variables on a scatterplot and informally describe how the data points are distributed and any apparent relationship that exists between the two variables (e.g., between time spent on homework and grade level). What it means for you: You’ll learn about different types of correlation and what they look like on scatterplots. • Key words: • slope • positive correlation • negative correlation • strong correlation

3. Lesson 6.2.2 Shapes of Scatterplots In the last Lesson, you learned how to make scatterplots from sets of data. By looking at the pattern of the points in a scatterplot, you can decide how the variables are related — for example, whether ice cream sales really do increase on hot days.

4. Variables are positively correlated if one variable increases as the other does. Lesson 6.2.2 Shapes of Scatterplots Positive Slope Means Positive Correlation If two things are correlated, they are related to each other — if one changes, the other will too. Two variables are positively correlated if one variable increases when the other does. For example, children’s heights are positively correlated with their ages — because older children are typically taller than younger ones.

5. Lesson 6.2.2 Shapes of Scatterplots If two positively correlated variables are plotted on a scatterplot, the points will lie in a band from bottom left to top right. If you were to draw a line through the points it would have a positive slope. This graph shows positive correlation. The thinner the band of points on the scatterplot, the more strongly correlated the data is. This graph shows strongpositive correlation.

6. Variables are negatively correlated if one variable increases as the other decreases. Lesson 6.2.2 Shapes of Scatterplots Negative Slope Means Negative Correlation Negative correlation is when one quantity increases as another decreases. For example, values of cars usually decrease as their age increases.

7. Lesson 6.2.2 Shapes of Scatterplots If a scatterplot shows negative correlation, the points will lie in a band from top left tobottom right. They’ll follow a line with a negative slope. This graph shows negative correlation. The thinner the band of points, the more strongly correlated the data is. This graph shows strongnegative correlation.

8. Lesson 6.2.2 Shapes of Scatterplots No Obvious Correlation Means Random Distribution When points seem to be spread randomly all over the scatterplot, then it is said that there is no obvious correlation. For example, people’s heights and their test scores are not correlated — the height of a person has no effect on their expected test score. This graph shows no obvious correlation.

9. 180 160 120 Number of ice creams sold 80 40 0 40 50 60 70 80 90 Temperature (°F) Lesson 6.2.2 Shapes of Scatterplots Example 1 Describe the correlation shown in the scatterplot opposite. Solution The plot shows positive correlation. (As the temperature increases, the number of ice creams sold tends to increase.) The correlation is fairly strong — the points lie in a fairly narrow band. Solution follows…

10. 180 180 160 160 120 120 Number of ice creams sold Number of ice creams sold 80 80 40 40 0 0 40 40 50 50 60 60 70 70 80 80 90 90 Temperature (°F) Temperature (°F) Lesson 6.2.2 Shapes of Scatterplots The correlation in Example 1 is strong, but it isn’t perfect. If it was perfect the points would lie in a straight line, as shown on the left.

11. 100 100 80 80 60 60 No. of cars using street A per day No. of burglaries per 1000 people 40 40 20 20 0 0 0 0 20 20 40 40 60 60 80 80 100 100 % of households with burglar alarms Amount of gasoline sold on street B per day ($) Lesson 6.2.2 Shapes of Scatterplots Guided Practice In Exercises 1–2, describe the type of correlation. 1. 2. negative no correlation Solution follows…

12. 100 5 90 4 80 3 Time spent on homework per day (h) Attendance (%) 70 2 60 1 50 0 0 20 40 60 80 100 0 2 4 6 8 10 Average test score (%) Grade level Lesson 6.2.2 Shapes of Scatterplots Guided Practice In Exercises 3–4, describe the type of correlation. 3. 4. positive strong positive Solution follows…

13. Lesson 6.2.2 Shapes of Scatterplots Independent Practice 1. Brandon investigates the relationship between the number of spectators at a football game and the amount of money taken at the concession stand. What kind of correlation would you expect? 2. If every job you do takes one job off your to-do list, what kind of correlation would you expect between the number of jobs you do and the number of jobs on your to-do list? positive negative Solution follows…

14. 100 50 80 40 30 60 No. of days absent from school Width of square (in) 20 40 10 20 0 0 0 0 20 20 40 40 60 60 80 80 100 100 Length of square (in) End of year test score Lesson 6.2.2 Shapes of Scatterplots Independent Practice In Exercises 3–4, describe the correlation shown. 3. 4. perfect positive correlation weak negative correlation Solution follows…

15. Negative correlation Positive correlation Lesson 6.2.2 Shapes of Scatterplots Round Up If the points lie roughly in a diagonal line across a scatterplot, it means the variables are correlated. An “uphill” band means positive correlation, whereas a “downhill” band means negative correlation.