Question

The line plots represent data collected on the travel times to school from two groups of 15 students. A horizontal line starting at 0, with tick marks every two units up to 28. The line is labeled Minutes Traveled. There is one dot above 4,6,14, and 28. There are two dots above 10, 12, 18, and 22. There are three dots above 16. The graph is titled Bus 47 Travel Times. A horizontal line starting at 0, with tick marks every two units up to 28. The line is labeled Minutes Traveled. There is one dot above 8, 9,18, 20, and 22. There are two dots above 6, 10, 12,14, and 16. The graph is titled Bus 18 Travel Times. Compare the data and use the correct measure of variability to determine which bus is the most consistent. Explain your answer.

Answer 1

To compare the consistency of the data for each bus, we need to look at the measures of variability. The most common measures of variability are the range and the standard deviation.

The range is the difference between the highest and lowest values in a dataset. For Bus 47, the range is 28 - 4 = 24. For Bus 18, the range is 22 - 6 = 16. Based on the range, Bus 18 appears to be more consistent, as the range of travel times is smaller.

However, the range can be misleading if there are extreme values in the dataset. A more reliable measure of variability is the standard deviation, which measures how spread out the data is around the mean (average).

To calculate the standard deviation for each bus, we would need to know the full dataset. However, we can make some general observations based on the line plots. For Bus 47, the dots are more spread out and there are more outliers (dots that are far from the others). For Bus 18, the dots are more clustered together and there are fewer outliers.

Based on these observations, we can conclude that Bus 18 is the most consistent in terms of travel times.