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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)

Load FactorsRevenue Passenger MilesAvailable Seat Miles
Mean81
Mean48,629,156
Mean58,077,063
Median81.43
Median47,904,518
Median58,227,952
Mode81.4381.43
ModeNONE
ModeNONE
Minimum72.29
Minimum36,997,641
Minimum47,817,552
Maximum87.15
Maximum62,915,780
Maximum65,566,709
Standard Dev3.9091975
Standard Dev5,477,877
Standard Dev3,929,729
Variance Dev15.281825
Variance Dev30,007,131,936,823
Variance Dev15,442,771,170,173

Table 2- Summary Statistics of American Airlines (Domestic)

Load FactorsRevenue Passenger MilesAvailable Seat Miles
Mean82.934
Mean6,624,897
Mean7,984,735
Median83.355
Median6,522,230
Median7,753,372
Mode84.56
ModeNONE
ModeNONE
Minimum74.91
Minimum5,208,159
Minimum6,734,620
Maximum89.94
Maximum8,277,155
Maximum9,424,489
Standard Dev3.972
Standard Dev720,158.571
Standard Dev744,469.8849
Variance Dev15.762
Variance Dev518,628,367,282.42
Variance Dev554,235,409,510.06

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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 increasing revenue passenger miles. However, Fig.1 also presents itself with a few outliers in the data which are not following the positive trend.

The data does not provide a reason for this, but, it can be interpreted that specific carriers may not be performing in tandem with the overall other carriers. On the other hand, American Airlines (see Fig.2) shows uniformity in their correlation with a steep upward rising gradient and also represents a positive correlation between the two values.

Figure 2- American Airlines (Domestic) Performance

References

Bureau of Transportation Statistics (BTS). (2017). Load factor, All Carriers- All Airports. Retrieved from https://www.transtats.bts.gov/Data_Elements.aspx?Data=5, on July 5th, 2017.

Global Airline Industry Program (GAIP). (2017a). Traffic and capacity by operating region. Retrieved from http://web.mit.edu/airlinedata/www/Traffic&Capacity.html, on July 5th, 2017. Global Airline Industry Program (GAIP). (2017b). Glossary. Retrieved from http://web.mit.edu/airlinedata/www/Res_Glossary.html, on July 5th, 2017.

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