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The Chicago Transit Authority thinks that excessive speed on its buses increases maintenance cost. It believes that a reasonable median time from O’Hare Airport to John Hancock Center is about 30 minutes. From the following sample data (in minutes) can you help them determine whether the buses have been driven at excessive speeds? If you conclude from these data that they have, what explanation might you get from bus drivers?
17 32 21 22
29 19 29 34
52 29 43 39
44 34 30 41
Well, based on the data provided, it does seem like the buses have been driven at excessive speeds. The median time from O'Hare Airport to John Hancock Center is supposed to be around 30 minutes, but the given times are mostly exceeding that.
As for an explanation from the bus drivers, well, I have a few humorous suggestions. Maybe they wanted to give passengers an exhilarating roller coaster experience instead of a regular bus ride. Or perhaps they thought they were auditioning for a racing movie and wanted to show off their skills. Another possibility is that they were trying to break the world record for the fastest bus ride, or they simply forgot that they were driving buses and not sports cars.
Of course, these explanations are just for laughs. In reality, it could be a variety of reasons like traffic, time pressure, or personal driving habits. But hey, at least we can find humor in the situation!
To determine if the buses have been driven at excessive speeds, we can calculate the median time from the given sample data and compare it to the expected reasonable median time of 30 minutes.
Step 1: Calculate the median
Arrange the given sample data in ascending order:
17, 19, 21, 22, 29, 29, 30, 32, 34, 34, 39, 41, 43, 44, 52
To find the median, we need to find the value that is in the middle. Since we have an odd number of data points (15), the median will be the middle value.
Median = 29 (in this case, the value in the 8th position)
Step 2: Compare the median to the expected reasonable median time
The calculated median time is 29 minutes, which is less than the expected reasonable median time of 30 minutes.
Conclusion:
Based on the given sample data, it appears that the buses have not been driven at excessive speeds since the median time is less than the expected reasonable median time.
Explanation for bus drivers:
Bus drivers can be informed that the data analysis shows that the buses have not been driven at excessive speeds. They can be praised for maintaining a reasonable speed and reminded of the importance of adhering to the speed limits to minimize maintenance costs.
To determine whether the buses have been driven at excessive speeds, we can analyze the sample data provided and calculate the median time for the bus trip from O'Hare Airport to John Hancock Center. If the calculated median time is significantly higher than the expected reasonable time of 30 minutes, it would indicate that excessive speeds have likely been involved.
To calculate the median time, we first need to arrange the data in ascending order:
17, 19, 21, 22, 29, 29, 30, 32, 34, 34, 39, 41, 43, 44, 52
Next, we find the middle value of the data set. Since we have 15 observations, the 8th value would represent the median. In this case, the 8th value is 32.
The calculated median time based on the sample data is 32 minutes.
Based on the calculated median time, it does not appear that the buses have been driven at excessive speeds since the median time is close to the expected reasonable time of 30 minutes.
However, if we were to conclude that the buses have been driven at excessive speeds, possible explanations from bus drivers could include:
1. Traffic conditions: The drivers may argue that heavy traffic or road congestion has caused them to drive faster to maintain the schedule.
2. Time pressure: The drivers might feel pressure to complete trips within a certain time frame, leading them to drive at higher speeds.
3. Inadequate scheduling: The drivers may claim that the bus schedules are unrealistic, forcing them to drive faster to make up for delays.
These explanations would need to be investigated further to address any potential issues with excessive speed and maintenance costs.