Descriptive statistics were calculated for each of four variables: opening weekend sales, total gross sales, number of release theaters, and amount of weeks in the top 60. The sample mean and median provide analysts with a measure of central location in regards to a portion of the data set. Range, sample variance, and sample standard deviation produce quantitative judgments about the variability of the data sampled from a larger population of observations. Outliers, as defined as being more or less than 3 standard deviations from the mean, did not exist when the data was thoroughly analyzed; although some movies did appear to perform abnormally high at first glance. A positive correlation exists between total gross sales and each of the other variables, albeit some were considerably stronger than others.
The sample mean was calculated by dividing the sum of the observation values by 10, or the number of observations. For opening weekend sales, a sample mean of the 10 chosen movies was $30.17 million. Total gross sales of all sampled films held a mean of $95.803 million. The two figures could allow a reader to draw a general conclusion that for a majority of the films, approximately 31.5% of total gross sales were made during a film’s debut weekend. The average number of theaters in which a movie was released is 2,482.4. A sample mean of 13.9 was calculated using the number of weeks the sampled movies were in the top 60 films.
The mean is usually used as a measure of central location. However, the average is extraordinarily sensitive to abnormally large or small observations (Anderson et al., 2011, p.90). When using data with extreme values, the median is desired because its calculation depends less on the broadness of the range. Arranging the data from smallest to largest values and choosing the middle value will find the median. If there are two middle values, it is computed by taking the mean of the two numbers. The median for opening weekend sales was $23.61 million. Total gross sales offered a median of $61.55 million, while the number of theaters produced a median of 2,924.5. Utilizing the data set to generate a median for the number of weeks a film reigned in the top 60 gave a result of 15 weeks. Each category appeared to have a couple significantly low values and produced relatively lower sample means than the calculation of the medians.
The range is a measure of variability that depicts the broadness of values in a data set. It is computed by finding the difference in the highest and lowest observations. The range of the first variable, opening weekend sales, is $102.63 million. Total gross sales’ data set has a range of $286.95 million. Number of theaters carries a range of 3,834. Finally, the last variable of weeks in top 60, contributed a range of 18.
The sample variance can give a more precise measure of variability within a data set because it employs all numerical values to compute the difference of each observation relative...