Mathematics
Grade 7
15 min
Scatter plots
Scatter plots
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1
Introduction & Learning Objectives
Learning Objectives
Identify independent and dependent variables in a given scenario.
Construct a scatter plot from a set of bivariate data.
Describe the general pattern (trend) shown in a scatter plot (positive, negative, or no correlation).
Interpret the strength of a linear relationship (strong, moderate, weak) from a scatter plot.
Identify outliers in a scatter plot.
Make reasonable predictions based on the trend observed in a scatter plot.
Have you ever wondered if there's a connection between how much time you spend playing video games and your test scores? 🎮📚 Let's learn how to visualize these kinds of relationships!
In this lesson, you'll discover how to create and interpret scatter plots, which are powerful graphs that show if two sets of data are...
2
Key Concepts & Vocabulary
TermDefinitionExample
Scatter PlotA graph that uses points to show the relationship between two different sets of data.A scatter plot showing the number of hours students slept versus their alertness levels in class.
Bivariate DataData that involves two different variables, often measured for the same item or individual.For each student, recording their height (variable 1) and their weight (variable 2).
Independent VariableThe variable that is changed or controlled, or that influences the other variable. It is typically plotted on the horizontal (x) axis.In a study of 'hours studied vs. test scores,' 'hours studied' is the independent variable.
Dependent VariableThe variable that is measured or observed, and whose value depends on the independent variable. It is typica...
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Core Formulas
Rule for Constructing a Scatter Plot
Each pair of bivariate data $(x, y)$ is plotted as a single point on a coordinate plane.
The independent variable ($x$) is always placed on the horizontal axis, and the dependent variable ($y$) is placed on the vertical axis. Ensure axes are labeled and scaled appropriately.
Rule for Identifying Correlation Direction
Observe the general trend of the points on the scatter plot to determine the direction of the relationship.
If points generally rise from left to right, it's a positive correlation. If points generally fall from left to right, it's a negative correlation. If points are scattered randomly with no clear direction, there is no correlation.
Rule for Assessing Correlation Strength
The closer the points cluster arou...
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Challenging
A scatter plot shows a strong negative correlation between a car's speed and its travel time for a fixed distance. The data points range from 20 mph to 60 mph. What is a reasonable, but potentially less accurate, prediction for the travel time at 80 mph?
A.The travel time will be greater than the time at 60 mph.
B.The travel time will be less than the time at 60 mph, following the trend.
C.The travel time will be exactly zero.
D.It is impossible to make any kind of prediction.
Challenging
A researcher finds a strong positive correlation between the number of firefighters at a fire and the amount of damage caused by the fire. Which statement is the best explanation for this correlation?
A.Firefighters are causing the damage, so sending fewer firefighters would be better.
B.The amount of damage is causing more firefighters to be sent to the scene.
C.third factor, the size of the fire, is causing both the number of firefighters and the amount of damage to increase.
D.The correlation is a coincidence and has no real-world meaning.
Challenging
A scatter plot shows a strong negative correlation between the altitude of a city and its average annual temperature. Which of the following is an INCORRECT interpretation of the data?
A.Cities at higher altitudes tend to be colder.
B.As altitude increases, average temperature tends to decrease.
C.city at a low altitude will likely have a high average temperature.
D.If a city's average temperature is high, it must be at a high altitude.
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