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# Mth410 Essay

1184 words - 5 pages

Descriptive statistics:
Opening Gross:
Several central tendency measures (i.e., mean, median, and mode) are calculated for opening gross in the Excel file. As can be seen in the below histogram, opening gross has a right tail (i.e., skewed to the right), so median would be a more appropriate central tendency measure than the mean. The median opening gross was 0.39; 50% of the opening gross values were less than 0.39, 50% were above 0.39. The skewness of opening gross was 3.43 indicating a right tail. The kurtosis of opening gross was 13.81 indicating a leptokurtic distribution.
The range of opening gross was 108.43, from 0.01 to 108.44. The standard deviation of opening gross was 18.87. ...view middle of the document...

28 indicating a right tail. The kurtosis of total gross was 12.32 indicating a leptokurtic distribution.
The range of total gross was 380.15, from 0.03 to 380.18. The standard deviation of total gross was 63.16. However, because the distribution was skewed, interquartile range (IQR), which is the range for the middle 50% of the values, would be a more appropriate measure of variability. The interquartile range for total gross was 47.03.
Total Gross Outliers:
Based on the box-plot, extreme values were 380.18 (Star Wars: Episode III), 287.18 (Harry Potter and the Goblet of Fire), 234.21 (War of the Worlds), 209.22 (Wedding Crashers), 205.28 (Batman Begins), and 186.22 (Mr. and Mrs. Smith). It is also suggested that values that are less than z-score of -3 or larger than z-score of +3 should be considered outliers. Using that criteria 380.18 (Star Wars: Episode III), 287.18 (Harry Potter and the Goblet of Fire), and 234.21 (War of the Worlds) can be considered outliers.
Number of Theaters:
Several central tendency measures (i.e., mean, median, and mode) are calculated for the number of theaters in the Excel file. As can be seen in the below histogram, the number of theaters has a right tail (i.e., skewed to the right), so median would be a more appropriate central tendency measure than the mean. The median was 410; 50% of values on the number of theaters were less than 410, 50% were above 410. The skewness of the number of theaters was 0.56 indicating a right tail. The kurtosis of the number of theaters was -1.35 indicating a platykurtic distribution.
The range of the number of theaters was 3905, from 5 to 3910. The standard deviation of the number of theaters was 1378.69. However, because the distribution was skewed or had extreme values, interquartile range (IQR), which is the range for the middle 50% of the values, would be a more appropriate measure of variability. The interquartile range for the number of theaters was 2580.75.

Number of Theaters Outliers:
No outliers were observed on the box-plot or using the z-score criteria.
Weeks in Top 60:
Several central tendency measures (i.e., mean, median, and mode) are calculated for weeks in top 60 in the Excel file. As can be seen in the below histogram, weeks in top 60 has a right tail (i.e., skewed to the right), so median would be a more appropriate central tendency measure than the...

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