The number of consumer complaints against the top U.S....

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.

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.

Key Concepts

Arithmetic Mean

The arithmetic mean is a measure of central tendency calculated by summing all the values in a data set and dividing by the number of values. It provides a single value that represents the typical magnitude of the data, but it can be heavily influenced by extreme values or outliers.

Median

The median is the middle value of a data set when the values are arranged in order. Unlike the mean, the median is robust against outliers and skewed data, making it a reliable indicator of central tendency in distributions that are not symmetric.

Outliers

Outliers are values that are significantly higher or lower than the majority of the data. They can distort measures like the mean, leading to averages that may not accurately reflect the overall trend or typical values in the data set, which is why considering their impact is essential in statistical analysis.

Rate Standardization

Rate standardization involves adjusting raw data to account for differences in scale or size, such as calculating complaints per 100,000 passengers instead of using absolute numbers. This process makes comparisons across different entities more meaningful by normalizing the data based on relevant factors.

Transcript

00:01 This question shows you a couple different airlines and the number of complaints that they get.

00:06 The first part asks you to just average the total number of complaints.

00:12 We know that the mean is x bar is the sum of the xs divided by n or the total number of data points that we have.

00:23 Using a calculator, we can sum up all these xs to find is 3003 ,484, and there are obviously 10.

00:33 10 data points.

00:34 So we know that x bar is 348 .4 complaints.

00:42 It also wants us to find the mean, or the median.

00:46 We know that when n is 10, the median is going to be the average between x5 and x6.

00:53 That's going to be, so x5 is the fifth highest and x6, 6 is the sixth highest.

00:59 And so we want to find that the middle of those two.

01:03 So we have x5.

01:05 And x6 finding the average that is going to be 350 these are already in order so 350 is the fifth highest plus 149 which is the sixth highest dividing that by two the median we now know is 249 .5 complaints now part b asks are these measures of central tendency really good are they relevant are they helpful well consider what we're measuring in our first column, we have, in our first row, we have delta airlines.

01:39 And in our very last row, we have alaska air.

01:42 Which do you think gets more passengers? obviously, delta flies a lot more people every day than alaska does.

01:50 So it's natural that they'll get a lot more complaints...

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