Free Report On Managerial Report Using Descriptive Statistics

Introduction

In this paper the basics of statistical analysis tools will be shown to investigate the financial success of the motion pictures. A set of observations is considered, which represents films and their financial characteristics as opening and total gross sales, the amount of theaters the movie was shown in, the number of weeks the motion picture was open, etc. Such techniques as descriptive statistics, standard normal distribution and z-score and association measures (correlation) are used in this research.

Body

We are given with the set of 100 movies; there are 6 variables in the data set:
Rank – the ID number of the movie in the data set
Movie Title – the name of the movie
Opening Gross – the amount of opening gross sales in US dollars
Total Gross – the amount of total gross sales in US dollars
Theaters – the number of theaters the movie was shown in
Weeks – the number of weeks the movie was shown in theaters
Begin with descriptive statistics on four quantitative variables (#3-6). The output of descriptive statistics includes measures of central tendency (mean, median) and measures of variability (range, standard deviation). The summary of the descriptives is given below in a table:

Descriptive Statistics: Opening Gross; Total Gross; Theaters; Weeks

Variable Mean StDev Minimum Median Maximum IQR
Opening Gross 30219994 33166537 31610 20962718 207438708 19979476
Total Gross 100348852 95827983 28835528 64055593 623357910 81105916
Theaters 3130,1 617,4 924,0 3114,5 4404,0 686,0
Weeks 15,730 5,574 5,000 14,500 35,000 8,000
We also visualize the distribution of each variable with frequency histograms to understand how close the distribution of each variable to the normal distribution is.
It seems that the distribution of Weeks is a little left skewed, the distribution of Theaters is right skewed, the distribution of total gross is also right skewed and the distribution of opening gross is also right skewed. Also, it may be seen that there are few outliers in the data, but this issue will be checked later. Now more about descriptive statistics:
The average amount of the opening gross sales is $30,219,994, the median value is $20,962,718 and the data is very dispersed around the mean, because the interquatile range is $19,979,476 and the standard deviation is $33,166,537 which is ever bigger than mean value. The minimum opening gross is $31,610, the maximum is $207,438,708
The average amount of the total gross sales is $100,348,852, the median is $64,055,593. This data is also much dispersed because IQR is $81,105,916 and standard deviation is $95,827,983. The minimum total gross sales is $28,835,528 and the maximum is $623,357,910
The average number of theaters is 3130.1, the median is 3114.5. The data is not such dispersed with the standard deviation of 617.4 and IQR of 686. The minimum theaters number is 924, the maximum is 4404.
The average number of weeks is 15.73, median is 14.5. The data is not dispersed – standard deviation is 5.574 and IQR is 8. The minimum number of weeks is 5, the maximum is 35.
Now consider the problem of outliers in our data set. Outliers indicate bad data. The presence of outliers in the data set may bias all statistical conclusions. It is known that the one of definitions for outliers is that the observation is outlier if it is 1.5*IQR lower than 1st quartile or 1.5*IQR higher than 3rd quartile. Calculate quartiles for all variables:

Variable Q1 Q3 IQR

Opening Gross 13612048 33591524 19979476
Total Gross 44927667 126033583 81105916
Theaters 2809,5 3495,5 686,0
Weeks 12,000 20,000 8,000
Hence the criterion of lower and upper bounds of “usual” data is:
The following films are outliers:
For further analysis this data should be excluded from the initial data set. There are 73 observations left.
The last step of this analysis is to investigate the relationship between the variables. Construct a correlation matrix given in the table below:

Correlations: Opening Gross; Total Gross; Theaters; Weeks

Opening Gross Total Gross Theaters
Total Gross 0,723
0,000
Theaters 0,323 0,278
0,004 0,014
Weeks -0,001 0,272 0,105
0,997 0,017 0,363
Cell Contents: Pearson correlation
P-Value
It’s seen that there is a strong positive correlation between Total Gross sales and Opening Gross sales (r=0.723, p-value is < 0.001). This means that the good opening gross means also good total gross sales and vice versa. The other associations are weak; some of them are even insignificant. The one and only useful conclusion is regarding the relationship between total gross and opening gross. Other variables are weakly correlated to each other or even not correlated.

References

Anderson, D.R., Sweeney, D.J., Williams, T.A., Camm, J.D., & Cochran, J.J. (2015). Essentials of statistics for business and economics. (7th ed.). Stamford, CT: Cengage Learning.
Moses, Lincoln E. (1986) Think and Explain with Statistics, Addison-Wesley, ISBN 978-0-201-15619-5 . pp. 1–3
Adèr, H. J.; Mellenbergh, G. J. & Hand, D. J. (2007). Advising on research methods: A consultant's companion. Huizen, The Netherlands: Johannes van Kessel Publishing. ISBN 90-79418-01-3.