Mathematics
Grade 8
15 min
Outliers in scatter plots
Outliers in scatter plots
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1
Introduction & Learning Objectives
Learning Objectives
Define what an outlier is in the context of a scatter plot.
Visually identify outliers on a scatter plot.
Describe the position of an outlier relative to the general trend of the data.
Explain how an outlier can influence the perceived trend or relationship between variables.
Suggest plausible real-world reasons for the existence of an outlier in a given data set.
Distinguish between an outlier and a data point that is simply at the extreme end of a trend.
Have you ever seen something that just doesn't fit in with everything else? 🤔 In data, these unusual points can tell us a lot!
This lesson will teach you how to spot these 'odd ones out,' called outliers, in scatter plots. You'll learn why they're important and what they can r...
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Key Concepts & Vocabulary
TermDefinitionExample
Scatter PlotA graph that displays the relationship between two different numerical variables for a set of data. Each point on the graph represents a pair of values.A plot showing students' study hours (x-axis) versus their test scores (y-axis).
OutlierA data point on a scatter plot that lies significantly far away from the general cluster or trend of the other data points.On a plot of height vs. weight, a point representing a very short person who is unusually heavy compared to others of similar height.
Trend (or Pattern)The general direction or relationship that the data points on a scatter plot seem to follow. This can be positive, negative, or no trend.If points generally go up and to the right, there's a positive trend.
Data PointA single piece of infor...
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Core Formulas
Visual Identification of Outliers
An outlier is a data point that appears to be isolated and significantly distant from the main group or pattern formed by the majority of other data points on a scatter plot.
To use this rule, visually scan the scatter plot for any points that stand out as unusually far from the rest of the data. Look for points that don't seem to follow the general trend or cluster.
Impact on Perceived Trend
Outliers can sometimes pull the perceived trend (like a line of best fit) towards themselves, making the relationship appear stronger, weaker, or even different than it would be without the outlier.
When you identify an outlier, consider drawing a mental 'line of best fit' both with and without that point. Observe how the outlier might &#...
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Challenging
A researcher is told to remove all outliers from a dataset before analysis. According to the tutorial, why might this be a poor strategy if done without investigation?
A.Because removing data points is always incorrect.
B.Because outliers can represent valid, important, and rare events that provide valuable insights.
C.Because removing outliers will always make the correlation weaker.
D.Because it is impossible to be certain which points are true outliers.
Challenging
Two scatter plots show the same data on house prices vs. square footage, but Plot B includes one extra point that Plot A does not. The line of best fit for Plot A has a strong positive slope. The line of best fit for Plot B has a slope near zero (it's almost flat). Where is the outlier in Plot B most likely located?
A.At a very high square footage and a very high price.
B.At a very low square footage and a very low price.
C.At a very high square footage but a very low price.
D.At an average square footage but an extremely high price.
Challenging
A scatter plot shows hours of video games played per week (x) and GPA (y), with a general negative trend. An outlier is found at (2 hours, 1.0 GPA). What is the combined effect and potential meaning of this outlier?
A.It strengthens the negative trend by showing a low GPA.
B.It weakens the negative trend and could suggest that for some students, low game time does not correlate with high GPA due to other factors.
C.It has no effect because the GPA is low.
D.It strengthens the negative trend because 2 hours is a low amount of time.
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