Question

One runner's times in the first six races of the year were 18.5, 18.2, 19, 18.75, 19.1, and 19 minutes. Another runner's times were 17.2, 18, 17.5, 18.75, 19, and 18.2 minutes. What are the range and mean of each runner's scores? Use your results to compare the runners' skills.

Answer 1

Runner 1 has times with a range of 0.9 minutes and a mean of approximately 18.758 minutes. Runner 2 has a range of 1.8 minutes and a mean of approximately 18.108 minutes. Runner 2 is more consistent and faster on average.

Step-by-step explanation:

To calculate the range and mean of each runner's scores, we first organize their times:

Runner 1: 18.5, 18.2, 19, 18.75, 19.1, 19

Runner 2: 17.2, 18, 17.5, 18.75, 19, 18.2

To find the range for each runner, we subtract the shortest time from the longest time:

• Runner 1: Range = 19.1 - 18.2 = 0.9 minutes
• Runner 2: Range = 19 - 17.2 = 1.8 minutes

To find the mean (average) time, we add up all the times and divide by the number of races:

• Runner 1: Mean = (18.5 + 18.2 + 19 + 18.75 + 19.1 + 19) / 6 ≈ 18.758 minutes
• Runner 2: Mean = (17.2 + 18 + 17.5 + 18.75 + 19 + 18.2) / 6 ≈ 18.108 minutes

Comparing the ranges and means, it seems that Runner 2 is more consistent with a tighter range and has a faster average time.