Mathematics
Grade 7
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.
Identify the independent and dependent variables for a scatter plot.
Accurately plot ordered pairs to create a scatter plot from given data.
Describe the general trend or pattern (correlation) shown in a scatter plot.
Distinguish between positive, negative, and no correlation.
Interpret the relationship between two variables based on 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? 🎮 Scatter plots help us visualize these kinds of relationships!
In this lesson, you'll learn how to create and interpret scatter plots, which are powerful tools for visualizing how two different sets of data relate to each other. Und...
2
Key Concepts & Vocabulary
TermDefinitionExample
Scatter PlotA graph that shows the relationship between two sets of data. Each pair of data values is plotted as a single point on a coordinate plane.A scatter plot showing the number of hours students slept versus their alertness levels in class.
Ordered PairA pair of numbers $(x, y)$ that represents a single point on a coordinate plane. The first number (x) corresponds to the horizontal axis, and the second number (y) corresponds to the vertical axis.If a student studied for 3 hours and scored 75, the ordered pair would be (3, 75).
X-axis (Independent Variable)The horizontal axis on a coordinate plane, typically representing the independent variable (the variable that is changed or controlled, or that influences the other variable).In a scatter plot of 'hours...
3
Core Formulas
Plotting Ordered Pairs on a Scatter Plot
Each data point is represented as an ordered pair $(x, y)$, where $x$ is the value from the independent variable (x-axis) and $y$ is the value from the dependent variable (y-axis).
To create a scatter plot, you take each pair of related data values and mark its position on the graph. The first value (x) tells you how far to move horizontally from the origin, and the second value (y) tells you how far to move vertically from that horizontal position.
Identifying Correlation from a Scatter Plot
Observe the general trend of the points:
1. **Positive Correlation:** Points generally rise from left to right.
2. **Negative Correlation:** Points generally fall from left to right.
3. **No Correlation:** Points are scattered without a clear...
5 more steps in this tutorial
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Challenging
A scatter plot shows a city's average daily temperature on the x-axis and its monthly electricity usage on the y-axis over a full year. The points form a U-shape. How would you describe the correlation?
A.strong positive correlation
B.strong negative correlation
C.No correlation
D.non-linear relationship
Challenging
A dataset shows a strong positive correlation between variable A and variable B. A researcher concludes that an increase in A *causes* an increase in B. Why might this conclusion be incorrect?
A.Positive correlations are always incorrect.
B.The correlation might be a coincidence, or a third, unobserved variable could be causing both A and B to increase.
C.The researcher should have looked for a negative correlation instead.
D.strong correlation means that B causes A, not the other way around.
Challenging
A scatter plot shows the age of a car in years (x-axis) and its value (y-axis), showing a negative correlation. A new point is added for a 40-year-old rare, classic car with a very high value. How does this outlier affect the interpretation of the correlation?
A.It strengthens the negative correlation because the car is very old.
B.It has no effect on the correlation.
C.It weakens the negative correlation, making the overall trend less clear.
D.It changes the correlation from negative to positive.
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