Essay Sample on the Statistical Analysis of the Frequent Flyers Program

The assignment is based on the statistical analysis of the frequent flyers program, League Baseball teams as well as comparison of the WWE and Marriot International financial performance. The frequent flyer program involves enrolment of 48 members as presented below. In addition, there are statistical outputs are interpreted for ease of understanding.

The Description of the shape of the data distribution, kurtosis and skewness statistics

The above table presents statistical analysis for the enrolment of members in frequent flyer program. In statistics, kurtosis is usually recognized as the peak or the sharpness of a frequency-distribution curve. It gives a simple to understand graph on the distribution, showing the low, high and the median values. Kurtosis can be presented as either positive or negative values.

Furthermore, it is a statistical measure that is used to demonstrate the distribution of the observed data that are almost equivalent to the mean. It is from time to time referred to as the volatility of volatility of statistics. Statistics for the frequent flier program show that there is a negative kurtosis value of -.295 which means that the distribution is more peaked than normal. On the other hand, skewness is commonly known as an asymmetry in a statistical distribution. It shows a curve that appears distorted either to the right to the left. Generally, skewness defines the extent to which a distribution differs from a normal distribution. From the above data output on Frequent Flyer Program, the distribution has a negative skew since it posses long tail in the negative direction which is -.003. This therefore, means that the left hand tail is longer than the right hand tail.

Data distribution presented in the box plot shows that there is a lager value at the middle and this is why the line across the chart is longer compared to the other two lines on the furthest ends. The larger value represents 50 percentile of data and this is equivalent to the mean value of 55.58. The two short lines are also known as the outliers, and they are in showing the minimum and maximum values. From the presentation, the lowest outlier value is having a value of 22.00 whereas the highest outlier is having a value of is 90.30. On the other the range for the frequent fliers program is 68.30. The variables in addition show positive skewness and kurtosis values as 0.871 and 1.105 respectively. The positive values of kurtosis and skewness show that the right hand tail is observed to be longer than the left hand tail.

The Major League Baseball teams compiled for 2003.

The second set of data that is analyzed focuses on the League Baseball Teams. It involves 30 major league baseball teams for 2003 season. Statistical analysis shows that among the 30 variables tested, there was no missing variable. From the analysis, mean, median and mode for League Baseball Teams values are 70.939, 68.980 and 19.6 respectively. Furthermore, other statistical tests are performed for 30 baseball salaries for 2003 season. These statistical tests are the standard deviation which can be interpreted to be 28.0606; variance statistical test performed gives a value of 787.398 as well as the standard error which is 5.1231.

The Box Plot for Team Salary Distribution

The distribution of baseball team salary in 2003

The above is a box plot for the distribution of baseball team salary for 2003. It shows that there is a normal distribution of the baseball salaries. The middle line I longer than both the upper and lower lines thus we can deduce that the heavier line lies at 70.939. However, the lower outlier is 19.6 and the upper outlier is 152.7 millions. From the plot box, we can also find that the range of baseball salaries is 133.1. This is obtained by getting the difference between the upper and lower outlier value, (152.7-19.6).

In general, the distance sandwiching the upper and lower outliers forms what we call the imter-quartile range (Upper quartile and lower quartile). The two short horizontal lines below and above the box are what represent the smallest and largest observed values. The circles at the top and bottom of the chart are defined as outliers. The cases of values do constitute more than 3 box length from the upper or lower edge of the box. They therefore form the so called extreme values in this data set. The variables in addition show positive skewness and kurtosis values as 0.871 and 1.105 respectively. The positive values of kurtosis and skewness show that the right hand tail is observed to be longer than the left hand tail.

Comparison of Financial Performance of WWE and Marriott International

WWE Marriott International

This section also focuses on the comparisons of the financial performance between two WWE and Marriott International. The statistical data presented shows that WWE variables tested for the two companies is 65 respectively. However, their means are different since WWE has a mean of 20.9024 while Marriott International has a mean 102.52862. Higher mean value for Marriot International indicates that its financial performance is better compared to WWE. Regarding median and mode, the findings show that WWE has a median of 20.89 along with mode of 21.29 which are less than the median for Marriott International which is 102.4 and mode of 100.710. This thus gives an impression that the financial performance of Marriott International seems to be much better than that of WWE. The variance for WWE is .74, a value which is less than the for Marriott International 2.45080.

Last but not least, the statistical analysis indicates that the skewness and kurtosis for WWE are.534 and -.313 respectively but for Marriot International, skewness value is 6.013 and kurtosis value is .622. What is more, range, minimum and maximum values for WWE are found to be 1.74, 20.150 and 21.890 respectively. On the other hand, the International Marriot has a range value of 12.220, whereas its minimum value is 97.840 and the maximum value is 110.060. Last of all, the sum of the values for WWE is 1358.660 while that for Marriott International is 6664.360. In summary, the values for Marriot International are higher than for WWE. This is a clear indication that financial performance Marriot International is better than for WWE.