Math Problem Statement
A scatterplot. A scatterplot has a horizontal axis labeled x from 0 to 50 in increments of 5 and a vertical axis labeled y from 0 to 320 in increments of 20. A series of plotted points lies between x equals 0 and x equals 50, loosely forming a line that rises from left to right and passes through the points left-parenthesis 8 comma 10 right-parenthesis and left-parenthesis 50 comma 260 right-parenthesis
Choose the point in the scatter plot above that is most likely an outlier.
Select the correct answer below:
(
3.5
,
13
)
(
3.0
,
12
)
(
47.5
,
256
)
(
19.0
,
154
)
Solution
Let's analyze the points given and the overall trend of the scatterplot.
- The points (8, 10) and (50, 260) indicate a line that rises from left to right.
- We know the point (8, 10) is on the plot, and (50, 260) is another point. These suggest that the general trend is an upward slope.
Now, let's evaluate each of the options:
-
(3.5, 13):
- This point is relatively close to the lower end of the x-axis (near 0), so it seems to fit the general trend of the line.
-
(3.0, 12):
- Similar to (3.5, 13), this point is also near the lower end of the x-axis and would likely fall close to the trend line.
-
(47.5, 256):
- This point is close to (50, 260), so it aligns with the trend of the line as well.
-
(19.0, 154):
- This point, when placed on the graph, would appear to be somewhat distant from the expected trend, especially as the points seem to rise more steeply after x = 8. The point seems a bit too far below the expected line.
Thus, the point that stands out as most likely being an outlier is (19.0, 154).
Answer:
(19.0, 154) is most likely the outlier.
Would you like a more detailed breakdown of how this point is identified as an outlier?
Here are some related questions to explore further:
- How can we calculate the slope of the line passing through the points (8, 10) and (50, 260)?
- What would the expected value of y be at x = 19 if the points followed the line exactly?
- How do you determine if a point is an outlier based on a scatterplot?
- How can we use regression to find the best-fitting line for a set of points?
- What other methods could you use to detect outliers besides visual inspection?
Tip: When detecting outliers, always consider how much the point deviates from the general trend or line formed by the other points.
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Math Problem Analysis
Mathematical Concepts
Statistics
Scatterplots
Outliers
Linear Relationships
Formulas
Slope formula: m = (y2 - y1) / (x2 - x1)
Theorems
Outlier identification using trend analysis
Suitable Grade Level
Grades 8-10