Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association.
Official wording from the Common Core State Standards for Mathematics (Β© 2010 National Governors Association Center for Best Practices and Council of Chief State School Officers). View on thecorestandards.org
Until now, most data students handled described one variable at a time, such as heights or test scores. Bivariate data pairs two measurements from the same subject, like hours of practice and free-throw percentage for each player, and a scatter plot shows every pair as a single point. Grade 8 students build these plots, choosing sensible scales, and then read the overall pattern they reveal.
The vocabulary is precise. If points tend to rise from left to right the association is positive; if they tend to fall it is negative; if no trend appears there is no association. A pattern that follows a straight line is linear, while one that bends, such as a curve that rises and then levels off, is nonlinear. Students also look for clusters (groups of points bunched together) and outliers (points far from the rest) and suggest what might explain them. Throughout, the language stays careful: an association between two variables does not prove that one causes the other.
Students sometimes connect points in order like a line graph. A scatter plot shows separate pairs; the trend is judged from the overall cloud.
Points can rise strongly and then level off. That is a positive but nonlinear association, and a straight line would describe it poorly.
Ice cream sales and sunburn cases rise together, but one does not cause the other. Both are linked to hot weather.
An outlier might be a recording error or a genuinely unusual case. It should be investigated and described, not just deleted.
A class records hours of sleep and reaction time (in milliseconds) for 10 students: (6, 330), (7, 300), (8, 270), (5, 360), (9, 250), (6.5, 315), (7.5, 290), (8.5, 260), (4, 380), (8, 400). Describe the association.
Answer: A strong negative linear association, with one outlier at (8, 400).
Collecting class data makes this standard come alive: arm span against height, hand length against shoe size, or minutes of reading against vocabulary quiz scores. Students plot their own points on a shared wall chart, which turns the discussion of trends, clusters and outliers into a discussion about real classmates.
Assessment items typically show a scatter plot and ask for the type of association, or ask which statement about an outlier or cluster is correct. Practice clear sentences that name both variables, for example 'as temperature increases, hot drink sales tend to decrease'.
Original questions written for this standard. Choose an option or type your answer, then press Check. Every question has a worked explanation.
Answer: D) Negative
When one variable increases as the other decreases, the association is negative.
Answer: A) Positive nonlinear
Height increases with age (positive), but growth slows and levels off, so the pattern curves and is nonlinear.
Answer: B) A point far away from the overall pattern
An outlier does not fit the pattern of the rest of the data, whether it is high, low or off to one side.
Answer: 3
15 - 12 = 3 points do not fit the trend.
Answer: D) The variables are associated, possibly because both rise with town population
Association does not show cause. A third variable, town size, likely drives both.
Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.
A full lesson with slides, activities and an exit ticket on scatter plots and association, pitched to grade 8 and editable in PowerPoint or Google Slides.
Make a lesson βA printable, differentiated worksheet on 8.SP.A.1 with an answer key, ready in about a minute.
Make a worksheet βTurn scatter plots and association into a quiz students answer online that marks itself, with a class summary for you.
Build a test βData that pairs two variables measured on the same subjects, such as each student's height and arm span. Scatter plots are the main way to display it.
No. In grade 8 association is described in words. The correlation coefficient is introduced in high school statistics.