Chapter 4, Problem 1E

Load factors 2016 The Research and Innovative Technology Administration of the Bureau of Transportation Statistics (www.TranStats.bts.gov/Data_Elements.aspx?Data=2) reports load factors (passenger-miles as a percentage of available seatmiles) for commercial airlines for every month from 2000 through May 2016. Here are histograms and summary statistics for the domestic and international load factors for this time period:

Compare and contrast the distributions.

To determine

Compare and contrast the distributions of domestic load factor and international load factor.

Explanation of Solution

Given info:

The data represents the histogram and summary statistics for the load factors of domestic and international commercial airlines for every month from 2000 through May 2016.

Justification:

Interpretation of the histogram of domestic load factor:

From the given histograms for the domestic load factor, the observed points are given below:

• The histogram consists of only one largest bar and this indicates that the distribution of domestic load factor is unimodal.
• The histogram shows that the length of the curve of the left hand tail is larger compared to the length of the curve of the right hand tail and this says that the shape of the distribution is skewed to left.

Interpretation of the histogram of international load factor:

From the given histograms for the international load factor, the observed points are given below:

• The histogram consists of only one largest bar and this indicates that the distribution of international load factor is unimodal.
• The histogram shows that the length of the curve of the left hand tail is larger compared to the length of the curve of the right hand tail and this says that the shape of the distribution is skewed to left.

Interpretation of the summary statistics of domestic and international load factors:

The median of the domestic load factor is 80.07 and the median of the international load factor is 78.86, the inter quartile range of the domestic load factor is 9.53 and the inter quartile range of the international load factor is 6.24.

Comparison and contrast:

• The distributions of both the data sets of domestic and international load factors are unimodal with left skewed.
• The distributions of international load factor may contain low outliers due to less variability.
• Median is an appropriate measure of centre, here the medians for both the distributions are close and this says that the distributions of domestic load factor and international load factor are almost similar.
• Inter quartile range is an appropriate measure for the spread of the distribution and the IQR of domestic load factor is high, which indicates that the variability is more in the domestic load factors.