Statistical Assignment

 





Statistical Assignment 




BACKGROUND
The current report quantitatively analyzes three variables – load factors, revenue passenger
mile, and available seat miles between American Airlines and U.S. major carriers (cumulatively).
The data retrieved for the analysis was extracted from the Bureau of Transportation Statistics
focusing on domestic flights from January 2006 to December 2012. The quantitative analysis
focused on finding critical statistical values like, mean, median, mode, standard deviation,
variance, and minimum/maximum of the variables. These values were calculated in Microsoft
Excel 2013 in order to compare American Airlines’ performance to the entire domestic industry.
The comparison was completed using summary statistics and scatter plots of the information that
are further presented below.
SUMMARY STATISTICS
Below are summary statistics for each of the data sets which had eighty-four (84) number
of values in the entire sample. The arithmetic mean was calculated using the following formula;
x_bar= (Σxi)/n. All major U.S. carriers had a load factor mean of 81% (see Table 1), while
American Airlines had a load factor mean of 82.934% (see Table 2). Passenger load factor is used
to measure the capacity utilization of airlines often times used to examine the effectiveness of 
airline carriers to fill up their seats and generate fare revenue (GAIP, 2017b). Based on the average
that was obtained American Airlines has a higher load factor that is above the industry mean. The
measures of central tendency – mode and median are also close to the average for all major US
carriers as they both equal 81.43%. While American Airlines has a median and mode of 83.355%
and 84.56% respectively. Again performing above industry average. However, this may indicate
that American Airlines is creeping closer to crush loading which is being witnessed on various
flights around the country (GAIP, 2017a).
Table 1- Summary Statistics of All Major U.S. Carriers (Domestic)
Summary Statistics
Load Factors Revenue Passenger Miles Available Seat Miles
Mean 81 Mean 48,629,156 Mean 58,077,063
Median 81.43 Median 47,904,518 Median 58,227,952
Mode 81.43 Mode NONE Mode NONE
Minimum 72.29 Minimum 36,997,641 Minimum 47,817,552
Maximum 87.15 Maximum 62,915,780 Maximum 65,566,709
Standard
Dev 3.9091975
Standard
Dev 5,477,877 Standard
Dev 3,929,729
Variance 15.281825 Variance 30,007,131,936,823 Variance 15,442,771,170,173
Table 2- Summary Statistics of American Airlines (Domestic)
Summary Statistics
Load Factors Revenue Passenger Miles Available Seat Miles
Mean 82.934 Mean 6,624,897 Mean 7,984,735
Median 83.355 Median 6,522,230 Median 7,753,372
Mode 84.56 Mode NONE Mode NONE
Minimum 74.91 Minimum 5,208,159 Minimum 6,734,620
Maximum 89.94 Maximum 8,277,155 Maximum 9,424,489
Standard Deviation 3.972
Standard
Deviation 720,158.571
Standard
Deviation 744,469.8849
Variance 15.762 Variance
518,628,367,282.42
Variance
554,235,409,510.06
On the other hand, revenue passenger mile measures traffic for an airline and is considered
the basic amount of production that an airline carrier is able to create (GAIP, 2017b). Looking at
the averages in both tables above cumulative major airliners produced the most revenue passenger
miles with $48 million USD while American Airlines produced 6.7 million USD. Lastly, available
seat miles are a measurement for airlines flight passenger capacity. Cumulatively, the industry
holds 58miilion of these seats while American Airlines has about 8 million in available seat miles.
Once again, those in cumulative industry is outperforming American Airlines domestically.
On the measurements - variance, it is used in a data set to measure how far apart they or
how each of the number pulled is considered the set or the mean. What this means is that variance
can be used to see how individual numbers may relate to each other within a data set instead of
arranging the data in quartiles. Both the variance of cumulative data and American airlines of load
factors is approximately the same estimated to about 15% and 16% respectively. There is not much
difference in the variance between American Airlines and all other major carriers flying
domestically based on load factor. However, variance differs greatly between the two when it
comes to revenue passenger miles. Overall, the cumulative industry is outperforming American
Airlines in all variables, although American Airlines has a greater load factor. 
Figure 1- Cumulative US Major Carriers (Domestic) Performance
To better analyze the two variables of significance: load factor and revenue passenger
miles, scatter plots were made and illustrate the relationship between the two variables in the
figures below. Both figures produce a positive correlation between the two variables. This suggests
that both variables are moving in tandem to each other with increasing load factor resulting in
increa