Jena is researching fuel consumption in cars - Leaving Cert Mathematics - Question 8 - 2022

A reasonable line of best fit should show the general trend of the plotted points. This line should start near the lower left corner of the scatterplot, curving gently upwards towards the upper right to reflect the overall positive correlation between city and motorway miles per gallon.

For car K, with a City value of 20, the Motorway value estimated from the line of best fit would be approximately 38. For car L, with a Motorway value of 60, the City value estimated would be around 33.

I would be more confident in my value for: K [✓] L [ ] Reason: The point for car K (20, 38) falls closer to the line of best fit, suggesting a more accurate estimate. Conversely, the estimate for car L is further away from the plotted points, indicating less confidence.

To find the correlation coefficient r, we can use the formula:

$r = \frac{n(\sum xy) - (\sum x)(\sum y)}{\sqrt{[n\sum x^2 - (\sum x)^2][n\sum y^2 - (\sum y)^2]}}$

Plugging in the values calculated from the data above will yield the final answer correct to three decimal places.

Given the scatterplot doesn’t show a clear linear trend, it suggests there is little to no correlation between F and S, indicating that the correlation coefficient r_{FS} is likely to be very close to 0.

The mean is 52, so the sum of the scores is 13 * 52 = 676. With S and M included, we have: 534 + S + M = 676, therefore S + M = 142. The median is 54, meaning S must be less than 54 and both S and M must be distinct from the other scores. Hence, the least value for S could be 55, and the greatest value could be 87.