1. 1 Lesson 6.2.1 Making Scatterplots

2. 2 Lesson 6.2.1 Making 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 use scatterplots to display sets of data. Key words: conjecture scatterplot scale axes

3. 3 Making Scatterplots Lesson 6.2.1 You’d expect some variables to be related to each other. For example, it might not be a surprise to learn that as grade level increases, so does the average amount of homework that’s set. Scatterplots are a way of displaying sets of data to see if and how the variables are related to each other.

4. 4 Making Scatterplots Some Things May Be Related to Each Other Lesson 6.2.1 Some variables are related to other variables. You can make conjectures, or educated guesses, about how things might be related. For example, The hotter the day is, the more ice cream will be sold. The faster you drive a car, the fewer miles you’ll get to the gallon. The older a child, the later his or her bedtime.

5. 5 Making Scatterplots You Can Collect Data to Test Your Conjecture Lesson 6.2.1 To see if your conjecture is correct, you first need to collect data. Average temperature of day (°F) Number of ice creams sold that day 41 16 63 67 55 80 73 101 70 100 90 1703673123114 48668779 For example, to see if it’s true that ice cream sales increase on hotter days, you need to find the average temperature for a number of days, and the number of ice creams sold on each of these days. You might end up with a table of data that looks like this:

6. 6 Making Scatterplots Example 1 Solution follows… Lesson 6.2.1 What data could you collect to test the conjecture “the taller a person, the bigger their feet?” Solution You would need to collect data on the heights of a set of people, and on the size of their feet.

7. 7 Making Scatterplots Guided Practice Solution follows… Lesson 6.2.1 1. What data would you need to collect to test the conjecture, “the older a child, the later his or her bedtime”? 2. Design a table in which to record this data. You would need to collect data on the ages of a set of children and on their bedtimes. Age of child (years) Time child goes to bed

8. 8 Making Scatterplots Mark Data Pairs on a Scatterplot Lesson 6.2.1 You can display two sets of data values on a scatterplot. The values need to be in pairs. A scatterplot is a really good way of seeing if the data sets are related — there’s a lot more on this in the next two Lessons.

9. 9 Making Scatterplots Lesson 6.2.1 Below is the scatterplot showing the number of ice creams sold against the temperature. Each cross represents a pair of data values — the number of ice creams sold on a day of a certain temperature. 180 160 120 80 40 0 9050607080 Temperature (°F) Number of ice creams sold There were 170 ice creams sold when the temperature was 90 °F. You can show that it doesn’t by putting a little “wiggle” in the axis. The scale doesn’t have to start at zero. There were 101 ice creams sold when the temperature was 73 °F.

10. 10 Making Scatterplots Scatterplots Have Two Axes With Different Scales Lesson 6.2.1 You have to think carefully about the scale of each axis. Each axis represents a different thing and is likely to have a different scale. Here’s how to choose a sensible scale for an axis. 1.Look at the minimum and maximum values of the data set. You have to choose a starting point and an ending point for the scale that fits all of the data. Your scale doesn’t have to start at zero. If it doesn’t, you include a little “wiggle,” as shown previously. 2.Choose a sensible step size. It must be small enough so that you can show your data clearly, but big enough to fit on your piece of paper. Don’t forget to label each axis clearly. Once you’ve done all this you can start plotting your data.

11. 11 Making Scatterplots Lesson 6.2.1 180 160 120 80 40 0 9050607080 Temperature (°F) Number of ice creams sold The temperatures in this example were all between 41 °F and 90 °F — so 40 °F and 90 °F were suitable start and end points. It made sense not to start the axis from zero. Look at the ice cream sales graph again: The temperatures only had a range of about 50 °F, so 5 °F steps were used. The number of ice creams sold had a much bigger range, so steps of 20 were used.

12. 12 Making Scatterplots Example 2 Solution follows… Lesson 6.2.1 Make a scatterplot of the data below relating people’s ages and heights. Age (years) Height (in) 10 45 19 67 4 31 6 43 10 51 8 46546547 141213 Solution The heights go from 31 in to 67 in. This range is larger, so the scale might go from 20 to 70 in steps of 5 inches. First you need to decide on a scale for each axis. The ages go from 4 to 19, so a scale might run from 0 to 20, in steps of 2. Then you can plot the values. Think of each pair of values as coordinates with the form ( age, height ), instead of ( x, y ). Solution continues…

13. 13 Making Scatterplots Example 2 Lesson 6.2.1 Make a scatterplot of the data below relating people’s ages and heights. Age (years) Height (in) 10 45 19 67 4 31 6 43 10 51 8 46546547 141213 Solution (continued) 60 50 40 30 20 0 481216 Age (years) Height (in) 70 (4, 31) (10, 45) (19, 67) The first three values in the table would be plotted at (10, 45), (19, 67), and (4, 31). The rest of the values can be plotted in the same way.

14. 14 Making Scatterplots Guided Practice Solution follows… Lesson 6.2.1 3. Use the data below to make a scatterplot relating foot length to height. Foot length (in) Height (in) 7 64 8 68 8.3 70.1 972 8.569 7.457 59 63 68 6.5 7.5 8.1 75 70 65 60 55 678910 Foot length (in) Height (in) Foot length (in) Height (in) 8.2 62 9.1 73 7.5 61 765 6.867 7.871 69 75 70 8.4 9.5 8.2

15. 15 Making Scatterplots Independent Practice Solution follows… Lesson 6.2.1 1. Miguel makes the conjecture, “the more people there are in a household, the heavier their recycling bins.” What data would you collect to test Miguel’s conjecture? You would collect data on the number of people in a set of households, and the weight of their recycling bins.

16. 16 Making Scatterplots Independent Practice Solution follows… Lesson 6.2.1 2. The data below was collected to test this conjecture: “The older a child, the less time he or she will sleep per day.” Draw a scatterplot of this data. 14 10 6 481216 Age (years) Hours of sleep 0 18 Age (years) Hours of sleep 4.5 64 0.5 68 8 70.1 1572 1169 1457 59 63 68 10.5 2 6

17. 17 Making Scatterplots Round Up Lesson 6.2.1 Now you know what a scatterplot is and how to draw one. The next Lesson shows you how to interpret scatterplots, and how to decide whether, or how closely, the variables are related.