Question

1. the following data was collected for a runner’s speed: 4 mi/hr, 3 mi/hr, 6.9 mi/hr, and 7 mi/hr.

a. is this data precise?
explain.
b. if the runner tends to run
5 mi/hr, is this data an
accurate representation of
the runner’s ability?
explain.

Explanation:

Part a

Precision in data refers to how close the measured values are to each other. Let's check the differences between the values: The differences between 4 and 3 is 1, between 4 and 6.9 is 2.9, between 4 and 7 is 3, between 3 and 6.9 is 3.9, between 3 and 7 is 4, between 6.9 and 7 is 0.1. The values (4, 3, 6.9, 7) have relatively large differences (except 6.9 and 7) and are not clustered closely together. So the data is not precise as the measured speeds vary significantly from one another.

Accuracy refers to how close a measured value is to the true (accepted) value. The runner's true (tended) speed is 5 mi/hr. Let's check the distances of each measured speed from 5: |4 - 5| = 1, |3 - 5| = 2, |6.9 - 5| = 1.9, |7 - 5| = 2. The measured speeds (4, 3, 6.9, 7) are not close to the true value of 5 mi/hr (with differences of 1, 2, 1.9, 2 mi/hr). So the data is not an accurate representation of the runner's ability.

Answer:

No, the data is not precise. Precision means the measured values are close to each other. The speeds (4 mi/hr, 3 mi/hr, 6.9 mi/hr, 7 mi/hr) have relatively large differences (e.g., 3 and 6.9 differ by 3.9 mi/hr) and are not clustered closely, so they lack precision.

Part b