Statistics on Movie DVD’s by David Gurney The data for this project came from the Movies Unlimited website www.moviesunlimited.com and the Critics Choice website www.ccvideo.com on July 3, 2011. The variables were the movie producer, the length of the move in minutes, the cost at Movies Unlimited and the cost at Critics Choice. When multiple producers were listed, the most well‐known was chosen. I decided Columbia and Universal were equally well‐known, and so listed them both for their joint production of the Electric Horseman. When multiple prices were listed, the lowest price was chosen. There were three different versions of “Close Encounters of the Third Kind” in theaters at one time or another, so the length of the original theatrical release was chosen. A frequency distribution for the producers is shown below and a bar chart follows.
Producer Frequency Relative Frequency 20th Century Fox 7 0.175 Alberto Grimaldi 1 0.025 Amblin Entertainment 1 0.025 Columbia Pictures 1 0.025 Columbia/Universal 5 0.125 Enigma Production 1 0.025 Horizon Pictures 1 0.025 Imagine Entertainment 1 0.025 Metro‐Goldwyn‐Mayer 6 0.150 Miramax Films 1 0.025 Orion Pictures 1 0.025 Paramount Pictures 1 0.025 Tig Productions 1 0.025 Touchstone Pictures 2 0.050 TriStar Pictures 2 0.050 Universal Pictures 1 0.025 USSR/Japan 1 0.025 Warner Brothers 6 0.150
8 Bar Chart of Producers 7 6 5 4 3 2 1 0 Fox
Pict. Pict. Pict. Pict. Pict.
Bros. Films Prod.
MGM
Enter. Enter.
Pictures Pictures Grimaldi
Cent.
A. USSR/Japan Productions
Horizon Warner Enigma Amblin Universal Orion Columbia 20th Imagine Miramax TriStar Tig Paramount Colum./Univers. Touchstone
20th Century Fox has the highest frequency at 7. Metro‐Goldwyn‐Mayer and Warner Brothers are tied for second with a frequency of 6. Columbia Pictures is alone in third with a frequency of 5. Touchstone Pictures and TriStar Pictures are tied for fourth and somewhat below the first three places with a frequency of 2. All the other producers occur just once. A chi‐square goodness of fit test was used to see if the producers were equally likely to occur. The resulting test statistic was 34.7 and the corresponding P‐value was 0.0068. So at 95% confidence, the evidence is strong enough to say that not all the producers are equally likely. The basic statistics for this data are shown in the table below.
Lengths Movies Unlimited Prices Critic’s Choice Prices mean 129.6 14.09 13.00 mode 105 (3 times) 12.74, 14.99 (6 times) 12.71 (15 times) minimum 81 8.99 5.92 first quartile 108 11.99 11.855 median 124.5 13.24 12.71 third quartile 139.5 15.99 12.735 maximum 200 29.99 25.46 range 119 21.00 19.54 standard deviation 28.3 4.02 3.98 interquartile range 31.5 4.00 0.88
The following is a histogram of the movie lengths. The maximum is 200 and the minimum is 81. The histogram is skewed right with a peak at 118. There are no gaps and no extreme values.
Histogram of Movie Lengths 18 16 14 12 10 8
Frequency 6 4 2 0 93 118 143 168 193 Length in Minutes
The histogram of the Movies Unlimited prices is shown below. The minimum is $8.99 and the maximum is $29.99. The histogram is skewed right with a single peak at $11.48. There is a gap at $26.48, but there are no extreme values.
Histogram of Movies Unlimited Prices 25
20
15
10 Frequency
5
0 $11.48 $16.48 $21.48 $26.48 $31.48 Price
The histogram of the Critic’s Choice prices is shown below. The minimum is $5.92 and the maximum is $25.46. The histogram is skewed to the right with one peak at $11.92. There is a gap at $19.92, but there are no extreme values.
Histogram of Critic's Choice Prices 25
20
15
10 Frequency
5
0 $7.92 $11.92 $15.92 $19.92 $23.92 Price
The following is a modified boxplot for the lengths of the movies in minutes. The boxplot is skewed right with two outliers on the high side at 191 and 200 minutes. Modified Boxplot of Movie Lengths
Modified Boxplots of DVD Prices
The median, third quartile and new maximum for Critic’s Choice are so close together that they are indistinguishable. Critic’s Choice has eight outliers on the low end and 9 outliers on the high end. Movies Unlimited only has one outlier on the high end. With the outliers, Movies Unlimited has the highest price and Critic’s Choice has the lowest price. But if the outliers are ignored, then Movies Unlimited still has the highest but also lowest price; in addition, Movies Unlimited has the largest range and interquartile range, and its median is larger than the Critic’s Choice median. A paired‐t test was used to determine if the means of the prices for Movies Unlimited and Critic’s Choice DVD’s are different. The test statistic was 2.73 and the resulting P‐value was 0.009. So at 95% confidence, the evidence is strong enough to say that the means of the prices for Movies Unlimited and Critic’s Choice are different. The 95% confidence intervals for the means of the quantitative variables are shown below. Movie Length (120.5, 138.6) Movies Unlimited Prices (12.80, 15.38) Critic’s Choice Prices (11.72, 14.27)
The three quantitative variables were tested to see if they were normally distributed using the Ryan‐ Joiner test. The tests were run at 95% confidence and since there are 40 films, the critical value for each of these tests is 0.972 according to Looney & Gulledge, The American Statistician, vol. 39, no. 1 (1985), pages 74 to 79. The test statistics for each of the variables are shown in the table below. Since each of the test statistics is less than the critical value, we can say with 95% confidence that each of the quantitative variables is not normally distributed. Variable Test Statistic Movie Length 0.965 Movies Unlimited Price 0.930 Critic’s Choice Price 0.919 The scatter diagram of the Movies Unlimited price versus the movie length is shown below.
Movies Unlimited Price Versus Movie Length $30
$25 Price
$20 Unlimited $15 Movies $10
$5 80 100 120 140 160 180 200 Movie Length
The equation of the regression line is: y = 0.0312x + 10.055 The regression line is the solid black line on the scatter diagram. The point at 110 minutes and $29.99 is the outlier. The point at 81 minutes and $16.99 is an influential observation.
The coefficient of determination is 0.048, which means that about 5% of the variation in the scatter diagram is determined by the regression line. The correlation coefficient of 0.219 signifies there is a weak positive correlation, which is supported by the scatter diagram.
Project Data Movie Name Producer Length Movies Critic’s (minutes) Unlimited Choice The Abyss 20th Century Fox 171 $14.99 $12.71 The African Queen Horizon Pictures 105 $16.99 $23.96 The Alamo Metro‐Goldwyn‐Mayer 162 $12.74 $12.73 Apollo 13 Imagine Entertainment 140 $12.74 $12.73 Awakenings Columbia Pictures 120 $ 9.99 $ 8.48 Bad Day at Black Rock Warner Brothers 81 $16.99 $16.96 Batteries Not Included Amblin Entertainment 107 $ 9.99 $ 5.93 Breaking Away 20th Century Fox 100 $ 8.99 $ 8.49 Broken Arrow (1996) 20th Century Fox 110 $ 9.99 $ 8.48 Cannery Row Metro‐Goldwyn‐Mayer 120 $16.99 $16.96 Chariots of Fire Enigma Productions 124 $12.74 $12.72 Cliffhanger TriStar Pictures 118 $ 9.99 $ 8.48 Close Encounters of the Columbia Pictures 135 $15.99 $16.96 Third Kind Con Air Touchstone 115 $21.59 $12.71 Cool Hand Luke Warner Brothers 126 $16.99 $16.96 Dances With Wolves Tig Productions 181 $16.99 $16.96 Derzu Uzalla USSR/Japan 110 $29.99 $25.46 Dirty Harry Warner Brothers 102 $11.99 $12.71 Doctor Zhivago Metro‐Goldwyn‐Mayer 200 $20.99 $12.71 Driving Miss Daisy Warner Brothers 99 $12.74 $12.71 Eddie and the Cruisers Metro‐Goldwyn‐Mayer 95 $12.74 $12.70 The Electric Horseman Columbia/Universal 121 $12.74 $12.71 The English Patient Miramax Films 162 $17.99 $16.96 Executive Decision Warner Brothers 133 $ 8.99 $ 5.92 Face Off Paramount Pictures 138 $14.99 $11.01 Father of the Bride (1991) Touchstone Pictures 105 $13.49 $12.74 First Knight Columbia Pictures 134 $14.99 $12.70 A Fish Called Wanda Metro‐Goldwyn‐Mayer 108 $14.99 $12.71 Fly Away Home Columbia Pictures 108 $11.99 $12.71 French Kiss 20th Century Fox 111 $ 8.99 $ 8.48 The Fugitive (1993) Warner Brothers 130 $11.99 $11.01 Ghandi Columbia Pictures 191 $15.99 $16.96 The Good, the Bad & Alberto Grimaldi 179 $13.49 $12.71 the Ugly Gorky Park Orion Pictures 127 $14.99 $12.71 The Grapes of Wrath 20th Century Fox 129 $12.99 $12.71 The Great Escape Metro‐Goldwyn‐Mayer 172 $13.49 $12.71 Independence Day 20th Century Fox 145 $14.99 $12.71 The Jackal Universal Pictures 125 $12.74 $12.71 Jerry Maguire TriStar Pictures 139 $11.99 $12.71 Jumping Jack Flash 20th Century Fox 105 $ 8.99 $ 8.48