boxplot - A graphic way of showing a summary of data using the median, quartiles, and extremes of the data.
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1 Learning Target Create scatterplots and identify whether there is a relationship between two sets of data. Draw a line of best fit and use it to make predictions. Focus Questions How can I organize data? Can I use this data to make a prediction? What does a point represent? Is there a connection between the two variables?
2 Vocab scatterplot - A way of displaying two-variable numerical data where two measurements are taken for each subject To create a scatterplot, the two values for each subject are written as coordinate pairs and graphed on a pair of coordinate axes (each axis representing a variable). line of best fit - A line of best fit shows a trend in the data representing where the data falls. This line does not need to touch any of the actual data points. Instead, it shows where the data generally falls. The line is a mathematical model of the data. boxplot - A graphic way of showing a summary of data using the median, quartiles, and extremes of the data. independent variable - When one quantity changes in a way that does not depend on the value of another quantity, the value that changes independently is represented with the independent variable. We often use the letter x for the independent variable. The independent variable is placed on the horizontal axis of a graph. dependent variable - When one quantity depends for its value on one or more others, it is called the dependent variable. We often use the letter y and the vertical y-axis for the dependent variable. (NOTE** In Statistics, the dependent variable is often called the response variable.)
3 C HOW MUCH IS THAT CAR? Team Whiparound a) Nate and Rick were discussing cars again. Nate claimed that cars with lower odometer readings were more expensive than cars with higher odometer readings. His evidence was that his car with 23,000 miles was worth more than Rick s car with 31,000 miles. To investigate Nate s claim, the boys collected data from several car advertisements and found the information in the table at right. b) Does the information in the table support Nate s claim? That is, do you believe Nate s claim that cars with a lower odometer reading cost more money?
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6 C Silent Debate Melissa looked at the data from problem 7-13 and said, I need to be able to see the data as a picture. I cannot tell if there is a relationship from the lists of numbers. She decided to use a box plot. Her box plots for odometer reading and price are shown below. Do these pictures help you decide if Nate is correct? Why or why not? What information does this give us? Do we know by looking at this plot if the car with the greatest price has the least number of miles?
7 C Red Light/Green Light Melissa wondered if a coordinate graph could help determine if there was a relationship in Nate s data from problem Follow the directions below to create a scatterplot of the data for Melissa or use 7-15 Student etool (Desmos). Click in the lower right corner of the graph to view it in full-screen mode. Set up a graph showing Odometer Reading on the x axis and Price on the y axis. Label equal intervals on each axis so that all of the data will fit on the graph. Plot the data points from problem a) Describe the scatterplot you just created. What do you notice about how the points are placed on the graph? Do you see any patterns? b) Place an additional point on your graph for Nate s car that has an odometer reading of 23,000 miles. Explain your strategy for deciding where to put the point. c) When a relationship exists, one way to help show a trend in the data is to place a line or curve that, in general, represents where the data falls. This line, sometimes called a line of best fit, does not need to touch any of the actual data points. Instead, it shows where the data generally falls. The line is a mathematical model of the data. Models of data help you describe the data more easily and help you make predictions for other cars with different mileages. d) With your team, decide where a line of best fit could be placed that would best model the data points. Are there any limits to where your line makes sense? e) Using the line of best fit, can you predict the price of a car with an odometer reading of 80,000 miles? If so, explain how the line of best fit helps. If not, explain why it is not helpful.
8 Pairs Check Sometimes what you know about relationships can help you predict what data will look like when it is graphed. For each situation below: Look at the scatterplots and use your experience to decide which statement fits each scatterplot. Decide if there is a relationship between the data. That is, as one quantity changes, does the other change in a predictable way? If there is a relationship, describe it in a sentence. If there is no relationship, explain why you think there is not one. a) How fast a dog can run and the length of the dog's fur. b) A person's age and their body temperature. c) The child's age and the size of his or her feet. d) Outdoor temperature and the percentage of people wearing long sleeve shirts.
9 Closure Did the graph that you created in problem 15 support the ideas that you stated in problem 13? How can a scatterplot and line of best fit help is see a relationship between car mileage and value? How can a line of best fit help us make predictions about the value of a car based on its mileage?
10 Line of Best Fit A line of best fit is a straight line drawn through the center of a group of data points plotted on a scatterplot. It represents a set of data for two variables. It does not need to intersect each data point. Rather, it needs to approximate the data. A line of best fit looks and behaves like the data, as shown in the example at right.
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