To analyze the scatterplot and determine which statement is true, let's evaluate each option step by step:
Scatterplot Analysis
- The scatterplot shows the heights of Ferris wheels (in meters) on the vertical axis and the years they were built (from 1980 to 2010) on the horizontal axis.
- There is a general upward trend in the data, indicating that Ferris wheel heights tend to increase over time.
- A line of best fit is drawn through the data points, which helps us understand the overall pattern.
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Option A: All Ferris wheels built before 1980 must have been less than 60 meters high.
- The scatterplot only shows data starting from the year 1980. There are no data points for years before 1980.
- Since we have no information about Ferris wheels built before 1980, we cannot make any conclusions about their heights.
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This statement cannot be verified or confirmed based on the given data.
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Option B: Based on the line of best fit, Ferris wheel heights increase about 25 meters every 10 years.
- The line of best fit shows a positive slope, indicating an increase in Ferris wheel heights over time.
- To estimate the rate of increase:
- From the line of best fit, observe the change in height over a 10-year period.
- Around the year 1980, the height is approximately 60 meters.
- Around the year 1990, the height is approximately 85 meters.
- The difference in height over 10 years is \( 85 - 60 = 25 \) meters.
- This suggests that Ferris wheel heights increase by about 25 meters every 10 years.
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This statement is consistent with the data.
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Option C: Each Ferris wheel is taller than all Ferris wheels that were built earlier.
- While there is a general upward trend in the scatterplot, not every Ferris wheel built in a later year is taller than all Ferris wheels built in earlier years.
- For example, some Ferris wheels built after 2000 are shorter than some built around 2000.
- The scatterplot shows variability, meaning that while heights generally increase over time, there are exceptions where later-built Ferris wheels are not taller than some earlier-built ones.
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This statement is not true.
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Option D: Each year, more Ferris wheels were built than the year before.
- The scatterplot does not provide information about the number of Ferris wheels built each year. It only shows the heights of Ferris wheels and the years they were built.
- We cannot infer anything about the number of Ferris wheels built each year from this data.
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This statement cannot be verified or confirmed based on the given data.
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Conclusion
The only statement that is supported by the scatterplot is
Option B.
Final Answer:
\[
\boxed{B}
\]
Parent Tip: Review the logic above to help your child master the concept of scatter plots and lines of best fit worksheet answer key.
