Motion Picture Industry

Case Problem 2: The Motion Picture Industry This case provides the student with the opportunity to use numerical measures to continue the analysis of the motion picture industry data first presented in Chapter 2. Developing and interpreting descriptive statistics such as the mean, median, standard deviation and range are emphasized. Five-number summaries and the identification of outliers are also of interest. Interpretations and insights can vary. We illustrate some below. Descriptive Statistics Variable N Mean SE Mean StDev Range Opening Gross 100 9. 8 1. 89 18. 87 108. 43 Total Gross 100 33. 04 6. 32 63. 16 380. 15 Number of Theaters 100 1278 138 1379 3905 Weeks in Top 60 100 8. 680 0. 639 6. 390 26. 000 Variable MinimumQ1 Median Q3 Maximum Opening Gross 0. 0100 0. 0625 0. 395 12. 49 108. 44 Total Gross 0. 0300 0. 375 5. 854 47. 69 380. 18 Number of Theaters 5. 00 45. 3 410 2732 3910 Weeks in Top 60 1. 000 3. 000 7. 00 13. 000 27. 000 Interpretation Opening Weekend Gross Sales. Th e mean opening weekend gross sales is $9. 38 million. The five-number summary is . 01, . 0625, . 395, 12. 49 and 108. 44. Thus the opening weekend gross sales is highly variable and ranges from a low of $10,000 to a high of $108. 44 million. 50% of the motion pictures had an opening weekend gross sales of $395,000 or less, and 25% had a relatively low opening weekend gross sales of $62,500 or less. The top 25% of the motion pictures had an opening weekend gross sales of $12. 9 million or more. Total Gross Sales. The mean total gross sales is $33. 04 million. The five-number summary is . 03, . 375, 5. 854, 47. 69 and 380. 18. Thus the total gross sales is also highly variable and ranges from a low of $30,000 to a high of $380. 18 million. 50% of the motion pictures had a total gross sales of $5. 854 million or less, and 25% had a relatively low total gross sales of $375,000 or less. The top 25% of the motion pictures had total gross sales of $47. 69 million or more. Number of Theater s.The mean number of theaters for motion pictures is 1278 theaters. The five-number summary is 5, 45. 3, 410, 2732 and 3910. Thus the number of theaters for a motion picture is also highly variable and ranges from a low of 5 theaters to a high of 3910 theaters. 50% of the motion pictures were shown in 410 or fewer theaters. 25% of the motion pictures were shown in 45 or fewer theaters. The top 25% of the motion pictures were shown in 2732 or more theaters. Number of Weeks in Top 60. The mean number of weeks in the top 60 for motion pictures is 8. 8 weeks. The five-number summary is 1, 3, 7, 13 and 27. Thus the number of weeks in the top 60 is also highly variable and ranges from a low of 1 week to a high of 27 weeks. 50% of the motion pictures were on the top 60 list for 7 or fewer weeks. 25% of the motion pictures were on the top 60 list for 3 or fewer weeks. The top 25% of the motion pictures were on the top 60 list for 13 or more weeks. General Observations. The data show that th ere is a wide variation in the performance of motion pictures for the four variables being studied.Motion pictures range from the low gross sales movies shown in relatively few theaters to the highly successful motion pictures with hundreds of millions in gross sales and playing in almost 4000 theaters. The profiles of motion pictures using the means and medians are shown below. |Profile |Mean |Median | |Opening Weekend Gross Sales |$ 9. 38 million |$ . 395 million | |Total Gross Sales |$33. 04 million |$ 5. 54 million | |Number of Theaters |1278 |410 | |Number of Weeks in Top 60 |8. 68 |7 | The relatively few extremely high performance blockbuster motion pictures tend to inflate the mean in the above profile calculations. The profile based the median gives a better picture of the middle or more typical performance characteristics in the motion picture industry. Outliers We will use outliers to identify the highly successful blockbuster motion pictures in the data set.Using Q3 + 1. 5(IQR) to identify the levels required to qualify as a high performance outlier, we have the following. Opening Weekend Gross Sales Q3 + 1. 5(IQR) = 12. 49 + 1. 5(12. 49 – . 0625) = $31. 13 million Total Gross Sales Q3 + 1. 5(IQR) = 47. 69 + 1. 5(47. 69 – . 375) = $118. 66 million Number of Theaters Q3 + 1. 5(IQR) = 2732 + 1. 5(2732 – 45. 3) = 6762 theaters Number of Weeks on the Top 60 List Q3 + 1. 5(IQR) = 13 + 1. 5(13 – 3) = 28 weeks There are no outliers in terms of the number of theaters or the number of weeks on the top 60 list.There were motion pictures that were high on these two variables, but not high enough to be considered outliers. However, there were six motion pictures that out performed the other motion pictures in terms of reaching outlier levels in opening weekend gross sales and total gross sales. These motions pictures are considered the â€Å"blockbuster† motion pictures in the data set. To be in this category the motion pictur e had an opening weekend gross sales greater than $31. 13 million and a total gross sales greater than $118. 66 millions.The six blockbuster motion pictures in this category ranked by total gross sales are as follows: |Motion Picture |Opening Gross Sales |Total |Number of |Weeks in Top 60| | |($ millions) |Gross Sales |Theaters | | | | |($ millions) | | | |Star Wars: Episode III |108. 4 |380. 18 |3,663 |19 | |Harry Potter and the Goblet of Fire |102. 69 |287. 18 |3,858 |13 | |War of the Worlds | 77. 06 |234. 21 |3,910 |19 | |Wedding Crashers | 33. 90 |209. 22 |3,131 |23 | |Batman Begins | 48. 5 |205. 28 |3,858 |18 | |Mr. and Mrs. Smith | 50. 34 |186. 22 |3,451 |21 | Star Wars: Episode III was the top motion picture in terms of both opening weekend gross sales and total gross sales for 2005. War of the Worlds was shown in the most theaters 3910 and Wedding Crashers, at 23 weeks, was the motion picture in this group with the longest run in the top 60 list.