The motion picture industry is a competitive business More t

The motion picture industry is a competitive business. More than 50 studios produce a total of 300 to 400 new motion pictures each year, and the financial success of each motion picture varies considerably. Gross sales for the opening weekend, the total gross sales, the number of theaters the movie was shown in, and the number of weeks the motion picture was open are common variables used to measure the success of a motion picture. Data collected for a sample of 100 motion pictures produced in 20XX are contained in the file named Movies, linked at the bottom of the page. Use all 100 data points.

Managerial Report
Prepare a report (see below) using the numerical methods of descriptive statistics presented in this module to learn how each of the variables contributes to the success of a motion picture. Be sure to include the following three (3) items in your report.

Descriptive statistics (mean, median, range, and standard deviation) for each of the four variables along with an explanation of what the descriptive statistics tell us about the motion picture industry.

Use the z-score to determine which movies, if any, should be considered high-performance outliers in each of the four variables. If there are any outliers in any category, please list them and state for which category they are an outlier. Describe which method you used to make your determination.

Descriptive statistics (correlation coefficient) showing the relationship between total gross sales and each of the other three variables. Evaluate the relationships between total gross sales and each of the other three variables. Use tables, charts, graphs, or visual dashboards to support your conclusions.

Write a report that adheres to the Written Assignment Requirements under the heading “Expectations for CSU-Global Written Assignments” found in the CSU-Global Guide to Writing and APA Requirements.  As with all written assignments at CSU-Global, you should have in-text citations and a reference page. An example paper is provided in the MTH410 Guide to Writing with Statistics, linked at the bottom of the page.

Your report must contain the following:

A title page in APA style.

An introduction that summarizes the problem.

The body of the paper should answer the questions posed in the problem by communicating the results of your analysis. Include results of calculations, as well as charts and graphs, where appropriate.

A conclusion paragraph that addresses your findings and what you have determined from the data and your analysis.

Submit your Excel file in addition to your report.

Rank	Movie Title	Opening Gross	Total Gross	Theaters	Weeks
1	Marvel\'s The Avengers	207,438,708	623,357,910	4,349	22
2	The Dark Knight Rises	160,887,295	448,139,099	4,404	21
3	The Hunger Games	152,535,747	408,010,692	4,137	24
4	Skyfall	88,364,714	304,360,277	3,526	17
5	The Hobbit: An Unexpected Journey	84,617,303	303,003,568	4,100	19
6	The Twilight Saga: Breaking Dawn Part 2	141,067,634	292,324,737	4,070	16
7	The Amazing Spider-Man	62,004,688	262,030,663	4,318	15
8	Brave	66,323,594	237,283,207	4,164	30
9	Ted	54,415,205	218,815,487	3,303	17
10	Madagascar 3: Europe\'s Most Wanted	60,316,738	216,391,482	4,263	19
11	Dr. Seuss\' The Lorax	70,217,070	214,030,500	3,769	21
12	Wreck-It Ralph	49,038,712	189,422,889	3,752	26
13	Lincoln	944,308	182,207,973	2,293	24
14	MIB 3	54,592,779	179,020,854	4,248	15
15	Django Unchained	30,122,888	162,805,434	3,012	20
16	Ice Age: Continental Drift	46,629,259	161,321,843	3,886	30
17	Snow White and the Huntsman	56,217,700	155,332,381	3,777	14
18	Les Miserables (2012)	27,281,735	148,809,770	2,927	14
19	Hotel Transylvania	42,522,194	148,313,048	3,375	22
20	Taken 2	49,514,769	139,854,287	3,706	20
21	21 Jump Street	36,302,612	138,447,667	3,148	15
22	Argo	19,458,109	136,024,128	3,247	28
23	Silver Linings Playbook	443,003	132,092,958	2,809	29
24	Prometheus	51,050,101	126,477,084	3,442	15
25	Safe House	40,172,720	126,373,434	3,121	14
26	The Vow	41,202,458	125,014,030	3,038	14
27	Life of Pi	22,451,514	124,987,023	2,946	35
28	Magic Mike	39,127,170	113,721,571	3,120	13
29	The Bourne Legacy	38,142,825	113,203,870	3,753	13
30	Journey 2: The Mysterious Island	27,335,363	103,860,290	3,500	20
31	Rise of the Guardians	23,773,465	103,412,758	3,672	20
32	Zero Dark Thirty	417,150	95,720,716	2,946	15
33	Flight	24,900,566	93,772,375	2,638	15
34	Think Like a Man	33,636,303	91,547,205	2,052	11
35	The Campaign	26,588,460	86,907,746	3,302	15
36	The Expendables 2	28,591,370	85,028,192	3,355	14
37	Wrath of the Titans	33,457,188	83,670,083	3,545	13
38	Jack Reacher	15,210,156	80,070,736	3,352	13
39	Dark Shadows	29,685,274	79,727,149	3,755	14
40	Parental Guidance	14,554,053	77,267,296	3,368	21
41	John Carter	30,180,188	73,078,100	3,749	16
42	Act of Valor	24,476,632	70,012,847	3,053	15
43	This Is 40	11,579,175	67,544,505	2,931	10
44	Contraband	24,349,815	66,528,000	2,870	9
45	Looper	20,801,522	66,486,205	2,993	14
46	Tyler Perry\'s Madea\'s Witness Protection	25,390,575	65,653,242	2,161	12
47	Battleship	25,534,825	65,422,625	3,702	11
48	Pitch Perfect	5,149,433	65,001,093	2,787	20
49	Mirror Mirror	18,132,085	64,935,167	3,618	20
50	Chronicle (2012)	22,004,098	64,575,175	2,908	18
51	Hope Springs	14,650,121	63,536,011	2,441	11
52	Underworld Awakening	25,306,725	62,321,039	3,078	7
53	The Lucky One	22,518,358	60,457,138	3,175	13
54	The Dictator	17,435,092	59,650,222	3,014	10
55	Total Recall (2012)	25,577,758	58,877,969	3,601	9
56	Titanic 3D	17,285,453	57,884,114	3,674	9
57	American Reunion	21,514,080	57,011,521	3,203	8
58	ParaNorman	14,087,050	56,003,051	3,455	20
59	This Means War	17,405,930	54,760,791	3,189	17
60	Project X	21,051,363	54,731,865	3,055	11
61	The Woman in Black	20,874,072	54,333,290	2,856	13
62	Paranormal Activity 4	29,003,866	53,921,300	3,412	11
63	The Devil Inside	33,732,515	53,261,944	2,551	11
64	The Odd Life of Timothy Green	10,822,903	51,854,875	2,717	22
65	Ghost Rider: Spirit of Vengeance	22,115,334	51,774,002	3,174	12
66	The Grey	19,665,101	51,580,236	3,208	12
67	Red Tails	18,782,154	49,876,377	2,573	20
68	The Possession	17,732,480	49,130,154	2,860	12
69	Diary of a Wimpy Kid: Dog Days	14,623,599	49,008,662	3,401	20
70	Sinister	18,007,634	48,086,903	2,542	12
71	Beauty and the Beast (3D)	17,751,905	47,617,067	2,625	16
72	Savages (2012)	16,016,910	47,382,068	2,635	9
73	The Best Exotic Marigold Hotel	737,051	46,412,041	1,298	25
74	Moonrise Kingdom	522,996	45,512,466	924	23
75	Here Comes the Boom	11,816,596	45,290,318	3,014	18
76	Red Dawn (2012)	14,276,668	44,806,783	2,781	13
77	The Three Stooges	17,010,125	44,338,224	3,482	18
78	Star Wars: Episode I - The Phantom Menace (in 3D)	22,469,932	43,456,382	2,655	15
79	Resident Evil: Retribution	21,052,227	42,345,531	3,016	8
80	The Cabin in the Woods	14,743,614	42,073,277	2,811	13
81	What to Expect When You\'re Expecting	10,547,068	41,152,203	3,021	11
82	Finding Nemo (3D)	16,687,773	41,128,283	2,904	18
83	End of Watch	13,152,683	41,003,371	2,780	17
84	Rock of Ages	14,437,269	38,518,613	3,470	9
85	Abraham Lincoln: Vampire Hunter	16,306,974	37,519,139	3,109	13
86	Lawless	10,001,982	37,400,127	3,138	13
87	The Guilt Trip	5,290,629	37,134,215	2,431	11
88	That\'s My Boy	13,453,714	36,931,089	3,030	5
89	Trouble with the Curve	12,162,040	35,763,137	3,212	12
90	The Watch	12,750,297	35,353,000	3,168	12
91	Frankenweenie	11,412,213	35,291,068	3,005	21
92	Step Up Revolution	11,731,708	35,074,677	2,606	10
93	Tyler Perry\'s Good Deeds	15,583,924	35,025,791	2,132	12
94	Monsters, Inc. (3D)	4,774,686	34,043,006	2,618	19
95	2016 Obama\'s America	31,610	33,449,086	2,017	13
96	House at the End of The Street	12,287,234	31,611,916	3,083	13
97	The Pirates! Band of Misfits	11,137,734	31,051,126	3,358	14
98	Joyful Noise	11,225,190	30,932,113	2,735	10
99	Chimpanzee	10,673,748	28,972,764	1,567	16
100	The Five-Year Engagement	10,610,060	28,835,528	2,941	8

Solution

“Expectations for CSU-Global Written Assignments”

The motion picture industry is a competitive business. More than 50 studios produce a total of 300 to 400 new motion pictures each year, and the financial success of each motion picture varies considerably. Gross sales for the opening weekend, the total gross sales, the number of theaters the movie was shown in, and the number of weeks the motion picture was open are common variables used to measure the success of a motion picture. Data collected for a sample of 100 motion pictures produced in 20XX are contained in the file named Movies, linked at the bottom of the page.

We have to find descriptive statistics of the following data.

We can find descriptive statistics by using MINITAB.

steps are :

START --> STAT --> Basic statistics --> Display descriptive statistics --> Variables : \'Opening Gross\' \'Total Gross\' Theaters Weeks --> Statistics : Mean, Standard deviation, First quartile, Median, Third quartile, Minimum, Maximum, Range --> graphs : select second option --> ok

We see output as follows,

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

Variable Mean StDev Minimum Q1 Median Q3
Opening Gross 30219994 33166537 31610 13612048 20962718 33591524
Total Gross 100348852 95827983 28835528 44927667 64055593 126033583
Theaters 3130.1 617.4 924.0 2809.5 3114.5 3495.5
Weeks 15.730 5.574 5.000 12.000 14.500 20.000

Variable Maximum Range
Opening Gross 207438708 207407098
Total Gross 623357910 594522382
Theaters 4404.0 3480.0
Weeks 35.000 30.000

From this result we can say that, the mean opening gross for data is 30219994.

The mean total gross for data is 100348852.

The mean thearters are 3130.1 and mean weeks are 15.730.

The Standard Deviation is a measure of how spread out numbers are.

Standard deviation for opening gross is 33166537.

Standard deviation for total gross is  95827983.

Standard deviation for theaters is 617.4

Standard deviation for 5.574

We need Q1 and Q3 for finding outliers of each of the four variables.

A median is the number separating the higher half of a datasample, a population, or a probability distribution, from the lower half.

Median for opening gross is 20962718.

Median for total gross is  64055593.

Median for theaters is 3114.5

and median for weeks is 14.500

Range of the data is the difference between largest observation and smallest observation.

Range for opening cross is  207407098.

Range for total gross is 594522382.

Range for theaters is 3480.0

and range for weeks is 30.000

Outlier :

An outlier is an observation that lies an abnormal distance from other values in a random sample from a population.

We can find outlier by using formula,

lower limit = Q1 - 1.5*IQR

upper limit = Q3 + 1.5*IQR

where IQR is inter quarttile range.

IQR = Q3 - Q1

Now we have to calculate these limits for all the four variables.

Outliers for opening gross :

That means for the variable opening gross if there exist a point below -16357166 and above 63560738 then that point will be called as outlier.

Similarly outliers for total gross, theaters and weeks are,

Here response variable is total gross and other three are independent variables.

We have to find correlation coefficient between total gross sales and each of the other three variables.

We have direct command in EXCEL to find correlation coefficient.

And the command is,

=CORREL(known y\'s, known x\'s)

where, y is response variable that is total gross and

x is independent variable that is opening gross, theaters and weeks.

correlation coefficient between  total gross and  opening gross is 0.9312.

correlation coefficient between  total gross and theaters is 0.5817.

correlation coefficient between  total gross and weeks is 0.4212

We see that the correlation coefficient between three variables and total gross is positive.

There is high correlation between total gross and  opening gross.

Q1	13612048
Q3	33591524
Q3-Q1	19979476
Q1-1.5*IQR	-16357166
Q3+1.5*IQR	63560738