For this analysis, it was used descriptive statistics of a data set with four variables in order to describe the performance of the motion picture industry. First, the study involved measures of Location which include: mean, median, mode. In addition, it was analyzed measures of variability of the data set which include: variance, range, and standard deviation. Moreover, the outliers movies were identified by calculating the z-score of each variable. Finally, it was measured the association between two variables (correlation coefficient) to understand the relationship between more than one variable. Four variables were examined, and the results are described as follows: a.Opening Weekend Gross Sales (OWGS):
From the sample data analyzed for OWGS, three outlier movies were identified: War of the World, Harry Potter and the Goblet Fire and Start Wars Episode III (3% of the data set). The graph 1 shows the trend for OWGS and the descriptive statistics results are displayed in table 1. The performance for this variable can be described as follows: •The average OWGS is $9.37 million, however, without the outliers the average is reduced to $6.69 million, the reduction in the average was significant (-29%) due to taking out the outliers. This confirmed the distortion added to the variable by these outlier points. •The range of OWGS goes from $0.01 million to $108.44 million, however, the median is 0.4 what means 50% of the movies have OWGS less than $0.4 million. This value is below the mean, and this is the reason why the Skewness is positive (equal to 3.43 for the entire sample and 1.93 w/o outliers). Excluding the outliers reduced the maximum value from $108 million to $50.34 million. •The sample variance and standard deviation are high (356.25 and 18.87) indicating that the values are significantly spread out from the mean. Nevertheless, excluding the outliers reduced considerably the variance and standard deviation to 119.48 and 10.93. •In the sample, 96% of the movies sold less than $50million during the first weekend, 70% sold less than $10million, 58% of the movies sold less than $1Million in the same period (see table 2). •Moreover, 87% of the OWGS ($819 million) were sold by movies in the fourth quartile. •The three outlier movies (3% of the sample) represented 31% of the sum of OWGS equivalent to $288 million, and 97 movies (97% of the sample) represented the balance of total OWGS (69%= $649 million). Table 1: Descriptive Statistics of OWGS for the sample (with and without five outlier movies).
Graph 1: Opening weekend gross sales trend
Table 2: Open Weekend Sales - Quartiles and Pencentiles
b.Total Gross Sales (TGS):
For the Total Gross Sales (TGS), three outlier movies were identified: War of the World, Harry Potter and the Goblet Fire and Start Wars Episode III, these are the same movies as the previous variable. For this variable, the descriptive statistics results are displayed in table 3 and the trend is shown in graph 2. The observations are as follows: •The average TGS is $33.04 million, however, without the outliers the average is reduced to $24.77 million, the reduction in the average was significant (-25%) due to taking out the outliers. This confirmed the distortion added to the variable by these outlier points. • The range of sales goes from $0.03 million to $380.15 million, and the sample variance is considerably high 3,989.78, indicating that the values are extremely spread out from the mean. On the other hand, excluding the outliers reduces the variance to 1,695.71, and reduces the maximum value from $380 million to $209.22 million. •Furthermore, the standard deviation is high, however, it went from 63.16 to 41.17 after the outliers were excluded, reducing the deviation from the mean. •In the sample analyzed, 76% of the movies sold less than $50million, 55% sold less than $10million, and 34% of the movies sold less than $1Million (see table 4). •...