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Lesson 3What a Point in a Scatter Plot Means

Let’s investigate points in scatter plots.

Learning Targets:

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

3.1 The Giant Panda

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

an image of a panda bear
“Giant Panda 2” by Sheila Lau via Wikimedia Commons. Public Domain.
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.

3.2 Weight and Fuel Efficiency

The table shows the weight and fuel efficiency of 18 different cars.

car weight (kg) fuel efficiency (mpg)
A 1,\!549 25
B 1,\!610 20
C 1,\!737 21
D 1,\!777 20
E 1,\!486 23
F 1,\!962 16
G 2,\!384 16
H 1,\!957 19
I 2,\!212 16
J 1,\!115 29
K 2,\!068 18
L 1,\!663 19
M 2,\!216 18
N 1,\!432 25
O 1,\!987 18
P 1,\!580 26
Q 1,\!234 30
R 1,\!656 23

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.

 
open applet in presentation mode
 

  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?

Are you ready for more?

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 showing the number of times a die was rolled and the number of 6s rolled
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.

3.3 Coat Sales

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

temperature (degrees Celsius) coat sales (dollars)
-5 1,550
-3 1,340
3 1,060
8 1,070
15 680
21 490
23 410
21 510
17 600
11 740
6 940
-2 1,390
a scatter plot showing temperatures in celcius and coat sales in dollars
  1. What does the point (15, 680) 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 (0, A) what would it represent? Use the scatter plot to estimate a value for A .
  5. What would a point at (B, 0) represent? Use the scatter plot to estimate a value for B .
  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 3 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 showing a strong correlation between the height in inches and weight in pounds of dogs

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.

Lesson 3 Practice Problems

  1. Here is a table and a scatter plot that compares points per game to free throw attempts for a basketball team during a tournament.

    player free throw attempts points
    player A 5.5 28.3
    player B 2.1 18.6
    player C 4.1 13.7
    player D 1.6 10.6
    player E 3.1 10.4
    player F 1 5
    player G 1.2 5
    player H 0.7 4.7
    player I 1.5 3.7
    player J 1.5 3.5
    player K 1.2 3.1
    player L 0 1
    player M 0 0.8
    player N 0 0.6
    a scatter plot showing a positive correlation between free throw attempts per game and points per game
    1. Circle the point that represents the data for Player E.
    2. What does the point (2.1,18.6) represent?
    3. In that same tournament, Player O on another team scored 14.3 points per game with 4.8 free throw attempts per game. Plot a point on the graph that shows this information.

  2. Select all the representations that are appropriate for comparing exam score to number of hours of sleep the night before the exam.

    1. Histogram
    2. Scatter plot
    3. Dot plot
    4. Table
    5. Box plot

  3. A cone has a volume of 36\pi cm3 and height h . Complete this table for volume of cones with the same radius but different heights.

    height (cm) volume (cm3)
    h 36\pi
    2h
    5h
    \frac h2
    \frac h5