Question

The number of consumer complaints against the top U.S. airlines in 2013 in given in the following table.

Airline	Complaints	Complaints per 100,000 Passengers Boarding
Southwest Airlines	397	0.34
Alaska Airlines	86	0.44
Delta Airlines	713	0.59
JetBlue Airways	192	0.63
AirTran Airways	130	0.73
SkyWest Airlines	217	0.80
Mesa Airlines	71	0.85
Endeavor Air	113	0.86
ExpressJet Airlines	319	0.96
Hawaiian Airlines	105	1.06
Virgin America	81	1.28
US Airways	806	1.42
American Eagle Airlines	303	1.70
American Airlines	1730	1.99
United Airlines	1935	2.14
Frontier Airlines	316	3.09

(a) By considering the numbers in the colum labeled "Complaints," caclulate 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 1

(a) Total number of complaints=397+86+713+192+130+217+71+113+319+105+81+806+303+1730+1935+316=7514

No. of airlines is 16

Mean number of complaints = 7514/16=469.625

Now arranging the number of complaints in a order (increasing), it would be

71, 81, 86, 105, 113, 130, 192, 217, 303, 316, 319, 397, 713, 806, 1730, 1935

Since the total number of data is a even number(16), the values at 8th and 9th place would be the middle values. The median would be the average of these two values, that is (217+303)/2= 260

(b)The mean found out above is meaningless because number of complaints do not pertain to any comparable number of passengers. These complaints relate to different number of passengers travelling with different airlines. The average would have been meaningful if they pertain to the same number of passsegers for all airlines.

(c) Complaints per 100,000 number of passengers arranged in increasing order would be as follows:

0.34, 0.44, 0.59, 0.63, 0.73, 0.80, 0.85, 0.86, 0.96, 1.06, 1.28,1.42, 1.70, 1.99, 2.14, 3.09

Number of data is 16 and the sum would be = 18.88

Mean= 18.88/16= 1.18

This is a meaningful average, because it relates to 100,000 passangers boarding each airline.

The middle data are 0.86 and 096 ( 8th and 9th values). Average would be (0.86+0.96)/2 =0.91

The median of this data is 0.91

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