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Problem 41 Hard Difficulty

The number of consumer complaints against the top U.S. airlines during the first six months of 2010 is given in the following table. Source: U.S. Department of Transportation.
a. By considering the numbers in the column labeled “Complaints,” calculate the mean and median number of complaints per airline.
b. Explain why the averages found in part a are not meaningful.
c. Find the mean and median of the numbers in the column labeled “Complaints per 100,000 Passengers Boarding.” Discuss whether these averages are meaningful.

Answer

a) 348.4
249.5
b) The averages found in the above are not meaningful because variation of the data is more or the range of the data is more when compared with the averages. The measurements are not at equal weights
c) 1.187
1.215

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Video Transcript

this question shows you a couple of different airlines and the number of complaints that they get the first part ask you to just average the total number of complaints we know that the mean is explores. Some of the X is divided by and the total number of ah, of data points that we have using a calculator, we can sum up all these exes to find that is 303,484 and they're obviously 10 data points. So we know that X bar is 348 0.4 complaints. It also wants us to find the mean are the median. Um, we know that when n is 10 the median is gonna be the average between X five and X six. That's gonna be so. X five is the fifth highest. Next 66 is the sixth highest. Um, and so we want to find that the middle of those two. So we have X five next six finding the average, um, that is gonna be 350. He's already in orders of 350 is the fifth highest plus 140 Niners with six highest dividing that by to the median we now know is 249 0.5 complaints now for PS. Are these measures of central tendency of really good other relevant? Are they helpful? Well, consider what we're measuring in our first column. We have our first real. We have Delta Airlines, and in our very last year we have Alaska Air. Which do you think gets more passengers? Obviously, Delta flies Ah, lot more people every day than Alaska does. So it's natural that they'll get a lot more complaints. What we're really after is how many complaints per passenger are these airlines getting because obviously more more passengers will correlate to more complaints. So this means that no, it's not a great measure of central tendency. And actually, we want to use what's the next column? Which is complaints per 10,000? Here we have complaints per 10,000 and asked us again to find the mean I mean, we already went over This is this some of X over N and is still 10 and now when we sum up, all of our exes will get 11.87 complaints per 100,000 so the mean that mean for every for these top 10 airlines is that on average they'll get 1.187 complaints per 1000 passengers. 100,000 passengers. Now what's the median again? Will find x five and x six thes aren't in orders. We gotta make sure that we're finding the right ones, but will have I think, x five that there's no now going from lowest to highest X 50.87 and x six is 1.56 If we do buy those way too, we'll get the median and we'll find that it is 1.215 Now, is this a better measure of central tendency? Well, yes. With this way of measuring complaints, we are taking into account that some airlines get a lot more than others. And when we take away that factor now, we give each airline equal weight. And so we're finding really the average amount of complaints, um, per airline per passenger and your final answer