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On the scatter diagram, draw a circle around the point representing this car - OCR - GCSE Maths - Question 6 - 2019 - Paper 5
Question 6
On the scatter diagram, draw a circle around the point representing this car. (d) By drawing a line of best fit, estimate the value of a car that is 6 years old. (... show full transcript
Worked Solution & Example Answer:On the scatter diagram, draw a circle around the point representing this car - OCR - GCSE Maths - Question 6 - 2019 - Paper 5
Step 1
By drawing a line of best fit, estimate the value of a car that is 6 years old.
Answer
To estimate the value of a car that is 6 years old using a line of best fit on a scatter diagram, follow these steps:
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Draw the Line of Best Fit: Begin by carefully plotting the data points on the scatter diagram. Next, draw a line that best represents the trend of these points. Ensure that the line has approximately equal numbers of points above and below it, indicating a balanced fit.
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Locate the Age of 6 Years: On the horizontal axis (which represents the age of the cars), find the point that corresponds to 6 years.
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Estimate the Value: From the point where the age of 6 intersects with the line of best fit, move vertically to the vertical axis (which represents the value of the cars). Read off the estimated value from this intersection point.
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Report the Estimate: For instance, if the intersection shows approximately £8,000, then the estimated value of a 6-year-old car would be £8,000.
Step 2
Explain the limitations of using the equation of the line of best fit to estimate the value of a car that is 16 years old.
Answer
When using the equation of the line of best fit to estimate the value of a car that is 16 years old, the following limitations should be considered:
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Extrapolation Risk: Estimating values outside the range of available data (e.g., beyond the age of cars represented in the scatter diagram) can lead to inaccuracies. The trend observed within the dataset may not hold for ages not previously observed.
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Changes in Market Trends: The value of cars can fluctuate due to economic factors, consumer preferences, and technological advances. Hence, the estimated value based on past data may not reflect current market conditions.
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Data Variability: The scatter diagram may include variations due to outliers or irregular data points that could skew the line of best fit, making it less reliable for certain estimates.
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Assumption of Linearity: The equation assumes a linear relationship. If the actual relationship is nonlinear, the predictions made by the line of best fit may be highly inaccurate.