Motion Picture Industry

III. Data Analysis
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).
• Moreover, 85% of the TGS ($2,819 million) were sold by movies in the fourth quartile.
• The Skewness is positive (equal to 3.28 for the entire sample and 2.71 w/o outliers), indicating that the majority of the TGS for the sample are in the lower range of data set and below the mean.
• The three outlier movies (3% of the sample) represented 45% of the sum of TGS equivalent to $1,502 million, and 97 movies (97% of the sample) represented the balance of total TGS (59%= $1,801 million).
Table 3: Descriptive Statistics of TGS for the sample (with and without three outlier movies). Graph 2: Total Gross Sales trend

Table 4: Total Gross Sales - Quartiles and Pencentiles c. Number of Theaters
For the variable “Number of Theaters” (NT), no outlier movies were identified. For NT the descriptive statistics results are shown in table 5 and the trend can be seen in graph 3. The remarks for this variable are as follows:
• The average NT that exhibited the movies was 1,278 theaters.
• Although the range of NT goes from 5 to 3,910 theaters, the median is 410 theaters, meaning that half of the movies in the sample were exhibited in 410 theaters or less.
• The sample variance and the standard deviation are significantly high 1,900,784 and 1,378 theaters, indicating that the values are enormously spread out from the mean.
• The Skewness is still positive, equal to 0.56, indicating that the majority of the NT are in the lower range of data set and below the mean.
• For the sample analyzed, 28 movies (above 72th percentile) were shown in more than 2,500 theaters. And below the 54th percentile were shown is less 1,000 theaters (see table 6).

Table 5: Descriptive Statistics of Number of Theaters exhibiting the movies.

Graph 3: Number of Theaters trend Table 6: Number or Theaters - Quartiles and Pencentiles d. Weeks in Top 60 (W60)
For the variable “Weeks in Top 60” (W60) no outlier movies were identified. For W60 the descriptive statistics results are displayed in table 7 and the trend can be shown in graph 4. The observations for this variable are as follows:
• The average W60 was 8.68 weeks.
• The range of data goes from 1 to 27 weeks, and the median is 7 weeks, meaning that half of the movies in the sample were in the top 60 position for less or equal than 7 weeks.
• The Skewness is still positive, but very close to zero, indicating that the majority of the points in the sample are around 8 weeks (close to the mean).
• For the sample analyzed, below the 37th percentile the movies were in top 60 for 1month or less, below the 54th percentile the movies were in top 60 for 2 months or less, and above the 77th percentile movies were in top 60 for more than 3 months (see table 8).

Table 7: Descriptive Statistics for Number of Weeks in Top 60.

Graph 4: Weeks in Top 60 trend

Table 8: Weeks in Top 60 - Quartiles and Pencentiles

IV. Correlation coefficient between Total Gross Sales and the other variables
Total gross sale is an important indicator to measure the success in the motion picture industry. In this case it was measured the relationship between the Total gross sales and the other variables by using the correlation coefficient approach. This approach is adopted to measure the relationship between more than two variables. Correlation coefficient ranges from -1 to +1. The closer the correlation to -1 or +1 indicates a strong linear relationship. The closer the correlation to zero, the weaker the relationship is.
It was found a strong relationship between the opening gross sales and the total gross sales. The correlation coefficient for these two variables is 0.96 indicating the greater the movie achieved in the opening gross sales the greater the total gross sales achieved by the movie in the overall exhibition period.
The graph 5 is a Scatter Diagram depicting a perfect positive linear relationship between these two factors.

Graph 5: Total Gross Sales versus Opening Week Gross Sales On the contrary, the relationship between total gross sales and weeks in top 60 indicates a positive linear relationship but not strong enough as the opening weekend gross sales, generating a correlation coefficient equal to 0.52. Although the relation between weeks in top 60 and the total gross sales is not strong, it could mean that for famous movies a significant amount of the audience attends to theaters during the first 2-3 weeks after their premier, therefore, the numbers of weeks in top 60 without additional information does not provide enough vision about the performance of a movie.
The graph 6 indicates the relationship between Total gross sales and the weeks in top 60.
Graph 6: Total Gross Sales versus Weeks in Top 60 Finally, for the relationship between the total gross sales and number of theaters there is a positive relationship between these two variables and it is clearly shown by the correlation coefficient which is equivalent to 0.70. The direct relation between TGS and number of theaters is much stronger than the relation between Total gross sales and weeks in top 60. This relation can be interpreted as the more number of theaters exhibiting the movie the higher total gross sales achieved, as shown in graph 7.
Graph 7: Total Gross Sales versus Number of Theaters

V. Conclusion
The study performed in this report used four different indicators for a sample of 100 movies made in 2005: Opening Weekend Gross Sales, Total Gross Sales, Number of theaters, and Weeks in Top 60 position.
From the samples of movies analyzed, three movies had outstanding performance and provided a significant impact to the analysis performed for the entire set of data:
1- Star Wars: Episode III: with gross sales of $108 million during the first weekend, and total gross sales of $380 million. Displayed in 3,663 theaters and 19 weeks in the top 60.
2- Harry Potter and the Goblet of Fire: with gross sales of $102 million during the first weekend, and total gross sales of $287 million. Displayed in 3,858 theaters and 13 weeks in the top 60.
3- War of the Words: with gross sales of $77 million during the first weekend, and total gross sales of $234 million. Displayed in 3,910 theaters and 19 weeks in the top 60.
However, those enormous figures don’t reflect the true performance for the movie industry in that year, 50% of the movies had gross sales less than $0.4 million during their first weekend and less than $5.6 million in total gross sales. In addition, these 3 movies were classified as science fiction and adventure movies, while the movies that classified as romance achieved low opening gross sales. Moreover, 50% of the movies were shown in less than 410 theaters across the country, for an average of only 8 theaters per state.
From the correlation coefficients analysis we can conclude that the gross sales performance during the first weekend is an explicit indicator of the total gross sales and success of the movie during the rest of their exhibition period. We found the same relationship between the number of theaters showing the movie and the gross sales obtained.
However, the relation between weeks in top 60 and the total gross sales was not strong, but the phenomena can be explained because for famous movies a significant amount of the audience attends to theaters during the first 2-3 weeks after their premier. For example Star wars Episode III sold 28% of its total gross sales in the first weekend. The variables analyzed do not provide visibility for the flow of audience, and this would be an important factor to consider.
Although these four variables provided a significant input in the analysis made, to be able to have a more comprehensive study, additional data for at least 5 years should be analyzed, also other variables that could impact the movie’s success should be considered as well, for example:
1- Number of tickets sold per week, to understand the flow of the audience along the exhibition period.
2- The actors in the movie, how famous they are. This variable could be measured by number of Oscar nominations or annual income for the cast.
3- The movie category such as action, adventure, drama, comedy, family, terror, romance.
4- Rating and how restrictive to the audience the movie is: G ( for all audience), PG-13 (above 13 years old), R (above 18 years old), etc.
5- Season displaying the movie, identifying whether external factors could impact the movie performance, for example: opening weekend during a snow storm, or a religious holiday.