Question

the dot plot shows predictions for the winning time in the 200 - meter sprint. the winner finished the race in 22.3 seconds. what is the greatest percent error among the predictions?
the greatest percent error among the predictions is
(round to the nearest tenth as needed.)

Explanation:

Step1: Find the prediction with the greatest absolute difference from the actual value

The actual winning time is \(22.3\) seconds.
For a prediction of \(22.8\) seconds:
The absolute difference \(d=\vert22.8 - 22.3\vert=0.5\) seconds.
For a prediction of \(22.2\) seconds: \(d = \vert22.2-22.3\vert = 0.1\) seconds.
For a prediction of \(22.4\) seconds: \(d=\vert22.4 - 22.3\vert=0.1\) seconds.
For a prediction of \(22.5\) seconds: \(d=\vert22.5 - 22.3\vert=0.2\) seconds.
For a prediction of \(22.6\) seconds: \(d=\vert22.6 - 22.3\vert=0.3\) seconds.
For a prediction of \(22.7\) seconds: \(d=\vert22.7 - 22.3\vert=0.4\) seconds.

Step2: Calculate the percent error

The formula for percent error is \(PE=\frac{\vert\text{Predicted}-\text{Actual}\vert}{\text{Actual}}\times100\%\)
Using the prediction of \(22.8\) seconds (since it has the largest absolute difference), \(\text{Actual}=22.3\) and \(\vert\text{Predicted}-\text{Actual}\vert = 0.5\)
\(PE=\frac{0.5}{22.3}\times100\%=\frac{50}{22.3}\%\approx2.2\%\)

Answer:

\(2.2\)