Math Problem Statement
Nate wants to predict how long people use the internet each day based on their age. The table below shows the age (in years) and average daily internet usage (in hours) for a sample of people. Age (years) [3] [10] [16] [22] [35] [55] Internet use (hours per day) [0.0] [1.0] [2.5] [4.0] [3.0] [0.5] All of the scatter plots below display the data correctly, but which one of them displays the data best? By convention, a good scatter plot uses a reasonable scale on both axes and puts the explanatory variable on the [x]-axis. Choose 1 answer: Choose 1 answer: (Choice A) Graph A A Graph A (Choice B) Graph B B Graph B (Choice C) Graph C C Graph C (Choice D) Graph D D Graph D Graph A provides Internet use, in hours, from 0 to 4, in increments of 1, on the y-axis, versus Age, in years, from 0 to 60, in increments of 5, on the x-axis. 6 points rise from (3, 0) to a maximum at (22, 4) before falling to (55, 0.5). All values estimated. [\small{10}] [\small{20}] [\small{30}] [\small{40}] [\small{50}] [\small{1}] [\small{2}] [\small{3}] [\small{4}] [~~~~] Graph B provides Internet use, in hours, from 0 to 14, in increments of 2, on the y-axis, versus Age, in years, from 0 to 150, in increments of 50, on the x-axis. 6 points rise from (3, 0) to a maximum at (22, 4) before falling to (55, 0.5). All values estimated. [\small{50}] [\small{100}] [\small{150}] [\small{2}] [\small{4}] [\small{6}] [\small{8}] [\small{10}] [\small{12}] [\small{14}] Graph C provides Age, in years, from 0 to 60, in increments of 5, on the y-axis, versus Internet use, in hours, from 0 to 4, in increments of 1, on the x-axis. 6 points create a leftward opening U-shape, falling from (0.5, 55) to (4, 22), and rising from (0, 4) to (4, 22). All values estimated. [\small{1}] [\small{2}] [\small{3}] [\small{4}] [\small{10}] [\small{20}] [\small{30}] [\small{40}] [\small{50}] [~~~~] Graph D provides Age, in years, from 0 to 150, in increments of 50, on the y-axis, versus Internet use, in hours, from 0 to 14, in increments of 2, on the x-axis. 6 points create a leftward opening U-shape, falling from (0.5, 55) to (4, 22), and rising from (0, 4) to (4, 22). All values estimated. [\small{2}] [\small{4}] [\small{6}] [\small{8}] [\small{10}] [\small{12}]
Solution
To determine which graph best displays the data, we need to consider two important factors:
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Explanatory variable on the x-axis: By convention, the explanatory variable (which in this case is age) should be placed on the x-axis, while the response variable (internet use in hours) should be on the y-axis.
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Reasonable scale: The scales on both axes should reasonably reflect the data range. In this case:
- The age values range from 3 to 55 years.
- The internet use values range from 0.0 to 4.0 hours per day.
Now, let's evaluate each graph:
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Graph A: Age is on the x-axis (from 0 to 60), and Internet use is on the y-axis (from 0 to 4). The scale is reasonable for both variables, making it easy to interpret the data.
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Graph B: Age is on the x-axis, but it goes from 0 to 150, and Internet use is on the y-axis, going from 0 to 14. These ranges are much larger than necessary, which makes it harder to see the variation in the data.
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Graph C: Internet use is on the x-axis and age is on the y-axis, which violates the convention of placing the explanatory variable (age) on the x-axis.
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Graph D: Similar to Graph B, it inverts the axis (age is on the y-axis and Internet use is on the x-axis) and uses an unnecessarily large range for both variables, making it difficult to interpret.
Best Choice: Graph A
Graph A displays the data correctly with a reasonable scale and the correct orientation of variables (age on the x-axis and internet use on the y-axis).
Would you like more details or have any questions?
Here are 5 related questions to expand this topic:
- How would the interpretation change if we reversed the axes?
- What type of correlation (positive or negative) can we observe from this scatter plot?
- Can a trendline be applied to this data? If yes, what type of regression would be best suited?
- How would the graph change if we added more data points with extreme ages (e.g., younger than 3 or older than 55)?
- How would a log scale affect the interpretation of the graph for internet use?
Tip: Always check the range of both axes to ensure the data is neither compressed nor stretched too much.
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Math Problem Analysis
Mathematical Concepts
Statistics
Scatter Plot Analysis
Explanatory and Response Variables
Formulas
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Theorems
Principle of Best Fit for Scatter Plots
Data Interpretation in Graphs
Suitable Grade Level
Grades 6-8
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