BA 303 - BUSINESS STATISTICS Week 2, Learning Unit 1 Discussion 1 Chapter 4, Problem 32
Chapter 4 Problem 32:
The Excel file Atlanta Airline Data provides arrival and taxi-in time statistics for one day at Atlanta Hartsfield International Airport. Find the mean and standard deviation of the difference between the scheduled and actual arrival times and the taxi-in time to the gate. Compute the Z-scores for each of those variables.
Here I have created a Histogram with the taxi times from the Atlanta Airlines Data. I created my own bins that I thought would show how the data is spread out best.
As you can see I found some of the descriptive statistics through excel. The mean is 11.60, the standard deviation is 5.495219, the median is 10, and the range is 44. These numbers give a lot of information about taxi times in the Atlanta airport. Firstly, the range is quite large but the mean is much lower. Since these are so different we can assume there are outliers that are making the range very large. This chart shows that the sample coefficient of skewness is 2.993014 but I also used another formula in excel and found 2.979434. These coefficients of skewness tell us that the data is positively skewed and has a high degree of skewness. We can also see that in positively skewed data the mean is the highest of the median and mode which is true in out data as well.
Chebyshev's theorem says that more than 75% of the data will be 2 standard deviations away from the mean and more than 88.9% of the data will be 3 standard deviations away. Since this theorem says that the data is more than these percentages it is true for this data. 95.51% of the data is within 2 standard deviations of the mean which is more than 75%. 97.01% of the data is within 3 standard deviations from the mean which is more than 88.9%.
The empirical rule has three statements about data which are 68% is within one standard deviation, 95% is within two standard deviations, and 99.7% is within three standard deviations. This rule give exact numbers so it is harder for the data to follow this. As stated before 95.51% percent of our data is within two standard deviations so that part is correct. However our data has 91.02% within one standard deviation and 97.01% within three standard deviations so this rule does not hold up with our data.
References
Evans, J. R. (2019). Chapter 4. In Business analytics (3rd ed.). Pearson.
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