Module 14: Background You’ll Need 2

  • Compute relative frequencies

Flight Frequencies

Research question: Do different airlines have the same distribution of flight status (whether the flight is on-time, delayed, canceled, or diverted)?

To answer this research question, we need to compare the distributions of a categorical variable for multiple populations. Our categorical variable will be flight status, and the populations we are comparing are the flights for different airlines. The values of our categorical variable are On-Time, Delayed, Canceled, and Diverted.

The following table is a two-way table (also called a contingency table), and it gives the counts for each value of the variable flight status for Delta Airlines and Southwest Airlines arrivals at the Atlanta airport in March 2021.[1] Notice that each row gives the distribution of flight status for an individual airline.

  On-Time Flights Delayed Flights Canceled Flights Diverted Flights Total
Delta Airlines 12,716 904 23 8 13,651
Southwest Airlines 2,240 299 22 1 2,562
For Delta Airlines, we can find the relative frequency of on-time flights, or the proportion of on-time flights, by looking at the ratio of on-time flights to the total number of flights:

[latex]\text{Relative Frequency} = \dfrac{\text{the number of times a value of the data occurs}}{\text{the total number of outcomes}}=\dfrac{12,716}{13,651}\approx0.9315[/latex]

So, about [latex]93.15\%[/latex] of Delta Airlines’ arriving flights in Atlanta in March 2021 were on time.

We can perform a similar computation for each value of the variable flight status to obtain the relative frequency distribution of flight status for Delta Airlines in terms of percentages, as shown in the following table.

  On-Time Percentage Flights Delayed Percentage Flights Canceled Percentage Flights Diverted Percentage Flights Total
Delta Airlines 93.15% 6.62% 0.17% 0.06% 100%

We can also consider the total number of flights for each value of the variable flight status and look at the overall relative frequency for each.

For example, there were [latex]12,716 + 2,240 = 14,956[/latex] on-time flights in total for both airlines. The total number of flights overall for both airlines was [latex]13,651 + 2,562 = 16,213[/latex] flights. Then, the overall relative frequency for on-time flights was:

[latex]\dfrac{14,956}{16,213}\approx0.92246962[/latex]

So, about [latex]92.25\%[/latex] of flights were on time for both airlines combined. In this case, we will keep more decimal places to avoid rounding errors in our next computations.

  1. U.S. Department of Transportation, Bureau of Transportation Statistics. (n.d.). On-time performance - Reporting operating carrier flight delays at a glance. https://www.transtats.bts.gov/HomeDrillChart_Month.asp?5ry_lrn4=FDFD&N44_Qry=E&5ry_Pn44vr4=DDD&5ry_Nv42146=DDD&heY_fryrp6lrn4=FDFE&heY_fryrp6Z106u=F ↵