Lesson 3What a Point in a Scatter Plot Means

Learning Goal

Let’s investigate points in scatter plots.

Learning Targets

  • I can describe the meaning of a point in a scatter plot in context.

Warm Up: The Giant Panda

Problem 1

A photo of a panda.

A giant panda lives in a zoo. What does the point on the graph tell you about the panda?

A point is graphed in the coordinate plane with the origin labeled “O”. The horizontal axis is labeled “age in months” and the numbers 0 through 84, in increments of 12, are indicated. The vertical axis is labeled “weight in kilograms” and the numbers 0 through 100, in increments of 25, are indicated. The point 36 comma 82 is indicated.

Activity 1: Weight and Fuel Efficiency

Problem 1

The table and scatter plot show weights and fuel efficiencies of 18 cars.

car

weight
(kg)

fuel efficiency
(mpg)

A

B

C

D

E

F

G

H

I

J

K

L

M

N

O

P

Q

R

open applet in presentation mode

The data points in the table are shown in this scatter plot.

You can hide the expressions list using the double arrow. You can click on a point to see its coordinates.

  1. Which point in the scatter plot represents Car L’s measurements? Drag the circle around the correct point.

  2. What is the fuel efficiency of the car with the greatest weight?

  3. What is the weight of the car with the greatest fuel efficiency?

  4. Car S weighs 1,912 kilograms and gets 16 miles per gallon. On the scatter plot, plot a point that represents Car S’s measurements.

  5. Cars N and O, shown in the scatter plot, are made by the same company. Compare their weights and fuel efficiencies. Does anything surprise you about these cars?

  6. A different company makes Cars F and G. Compare their weights and fuel efficiencies. Does anything surprise you about these cars?

Print Version

The table and scatter plot show weights and fuel efficiencies of 18 cars.

car

weight
(kg)

fuel efficiency
(mpg)

A

B

C

D

E

F

G

H

I

J

K

L

M

N

O

P

Q

R

A scatterplot with 20 data points. The horizontal axis is labeled “weight, in kilograms” and the numbers 1,000 through 2,500, in increments of 250, are indicated. The vertical axis is labeled “fuel efficiency, in miles per gallon” and the numbers 14 through 32, in increments of 2, are indicated. The graph shows the trend of the 20 data points moving linearly downward and to the right. The approximate coordinates of 11 selected data points are as follows: 1,130 comma 28. 1,240 comma 30. 1,400 comma 25. 1,490 comma 23. 1,550 comma 25. 1,590 comma 26. 1,650 comma 19. 1,740 comma 21. 1,775 comma 20. 1,950 comma 19. 2,200 comma 16.

  1. Which point in the scatter plot represents Car L’s measurements?

  2. What is the fuel efficiency of the car with the greatest weight?

  3. What is the weight of the car with the greatest fuel efficiency?

  4. Car S weighs 1,912 kilograms and gets 16 miles per gallon. On the scatter plot, plot a point that represents Car S’s measurements.

  5. Cars N and O, shown in the scatter plot, are made by the same company. Compare their weights and fuel efficiencies. Does anything surprise you about these cars?

  6. A different company makes Cars F and G. Compare their weights and fuel efficiencies. Does anything surprise you about these cars?

Are you ready for more?

Problem 1

After a board game competition, the tournament director collects 50 dice from the games played and rolls each one until he gets bored and tries a different one. The scatter plot shows the number of times he rolled each die and the number of 6s that resulted during those rolls.

A scatter plot of number of times the die is rolled (horizontal from 0-200) vs number of 6's (vertical from 0-40). Data starts at (50, 8.5) and goes up and to the right.

Select a point in the scatter plot and give its approximate coordinates, then tell the story of that point in the context of the problem.

Activity 2: Coat Sales

Problem 1

A clothing store keeps track of the average monthly temperature in degrees Celsius and coat sales in dollars.

temperature (degrees Celsius)

coat sales (dollars)

A table of data for temperature (degrees celsius) and coat sales (dollars) and then shown on a scatter plot.

  1. What does the point represent?

  2. For the month with the lowest average temperature, estimate the total amount made from coat sales. Explain how you used the table to find this information.

  3. For the month with the smallest coat sales, estimate the average monthly temperature. Explain how you used the scatter plot to find this information.

  4. If there were a point at what would it represent? Use the scatter plot to estimate a value for .

  5. What would a point at represent? Use the scatter plot to estimate a value for .

  6. Would it make sense to use this trend to estimate the value of sales when the average monthly temperature is 60 degrees Celsius? Explain your reasoning.

Lesson Summary

Scatter plots show two measurements for each individual from a group. For example, this scatter plot shows the weight and height for each dog from a group of 25 dogs.

A scatter plot of dog height (in) (horizontal from 6-30) vs dog weight (pounds) (vertical from 0-112). The data trends up and towards the right.

We can see that the tallest dogs are 27 inches, and that one of those tallest dogs weighs about 75 pounds while the other weighs about 110 pounds. This shows us that dog weight is not a function of dog height because there would be two different outputs for the same input. But we can see a general trend: Taller dogs tend to weigh more than shorter dogs. There are exceptions. For example, there is a dog that is 18 inches tall and weighs over 50 pounds, and there is another dog that is 21 inches tall but weighs less than 30 pounds.

When we collect data by measuring attributes like height, weight, area, or volume, we call the data numerical data (or measurement data), and we say that height, weight, area, or volume is a numerical variable. Upcoming lessons will discuss how to identify and describe trends in data that has been collected.