Question

EASY MIDDLE SCHOOL 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 10,16,20, and 28. There are two dots above 8 and 14. There are three dots above18. There are four dots above 12. The graph is titled Bus 14 Travel Times.

Compare the data and use the correct measure of variability to determine which bus is the most consistent. Explain your answer.

Bus 47, with an IQR of 8
Bus 14, with an IQR of 6
Bus 47, with a range of 8
Bus 14, with a range of 6

Answer 1

The bus with the smallest IQR is the most consistent. In this case, Bus 14 with an IQR of 6 demonstrates more consistent travel times as compared to Bus 47 with an IQR of 8.

Step-by-step explanation:

To determine which bus is the most consistent in terms of travel times, we need to look at the measure of variability. In this context, consistency can best be judged by the interquartile range (IQR), as it measures the spread of the middle 50% of data, minimizing the impact of potential outliers. The line plots given show the travel times for two different buses with different IQRs.

For Bus 47, the IQR is given as 8, and for Bus 14, the IQR is 6. A smaller IQR indicates that the middle 50% of travel times are closer together, suggesting more consistency in travel times. Thus, Bus 14, with an IQR of 6, is the most consistent.

The range, on the other hand, measures the overall spread of the data, from the smallest to the largest value. While useful, this is more affected by extreme values and might not be the best measure of consistency when typical, daily travel times are considered. Hence, among the options provided, the IQR is the correct measure to use for consistency.