Mathematics
Grade 8
15 min
Scatter plots
Scatter plots
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1
Introduction & Learning Objectives
Learning Objectives
Define what a scatter plot is and its purpose.
Construct a scatter plot from a given set of bivariate data.
Identify and describe positive, negative, and no correlation in scatter plots.
Assess the strength of a linear correlation (strong or weak).
Identify outliers in a scatter plot.
Informally draw a line of best fit (trend line) on a scatter plot.
Use a line of best fit to make predictions about data trends.
Ever wonder if there's a connection between how much you study and your test scores? 📚 Or if warmer weather means more ice cream sales? 🍦 Let's discover how to visually explore these kinds of relationships!
In this lesson, you'll learn about scatter plots, powerful graphs that help us see if there's a relationship, or corre...
2
Key Concepts & Vocabulary
TermDefinitionExample
Scatter PlotA graph that displays the relationship between two sets of numerical data by plotting individual data points as ordered pairs on a coordinate plane.A scatter plot showing the heights and weights of students in a class, where each point represents one student's height and weight.
CorrelationA statistical measure that expresses the extent to which two variables are linearly related (meaning they change together at a constant rate). It describes the direction and strength of the relationship.If a scatter plot shows that as temperature increases, ice cream sales also increase, there is a correlation between temperature and sales.
Positive CorrelationA relationship between two variables where both variables tend to increase or decrease together. On a scat...
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Core Formulas
Rule for Plotting Data Points
Each pair of data values $(x, y)$ from a dataset is plotted as a single point on the coordinate plane, where the x-axis represents the independent variable and the y-axis represents the dependent variable.
This rule ensures that each observation is correctly represented on the graph, forming the visual pattern of the scatter plot.
Rule for Interpreting Positive Correlation
If the points on a scatter plot generally rise from the lower-left to the upper-right, it indicates a positive correlation. This means as the x-variable increases, the y-variable tends to increase.
Use this rule to identify relationships where both variables move in the same direction. The closer the points are to forming a straight line, the stronger the positive correlation....
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Challenging
A scatter plot of 20 data points shows a weak positive correlation. An outlier is located in the upper-left corner of the plot. What is the most likely effect on the line of best fit if this outlier is removed?
A.The slope of the line will increase, and the positive correlation will appear stronger.
B.The slope of the line will decrease, and the correlation will become weaker.
C.The line of best fit will not change its position or slope.
D.The correlation will change from positive to negative.
Challenging
A city analyst finds a strong positive correlation between the number of firefighters responding to a fire and the dollar amount of damage caused by the fire. The analyst concludes that sending more firefighters causes more damage. Why is this conclusion flawed?
A.The correlation is actually negative, not positive.
B.The data used for the scatter plot is likely inaccurate.
C.Causation can only be determined by identifying outliers, not the trend.
D.third variable, the initial size of the fire, is causing both the number of firefighters and the amount of damage to increase.
Challenging
The line of best fit for a scatter plot showing the value of a collectible toy (y, in dollars) over time (x, in years since 2010) is y = 25x + 10. What is the best interpretation of the slope, 25?
A.The toy's initial value in 2010 was predicted to be $25.
B.The toy's value is predicted to increase by $25 each year.
C.The toy will be worth exactly $25 after 10 years.
D.The maximum predicted value of the toy is $25.
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