Question

The movie industry is a competitive business. The opening weekend gross sales ($ millions), the total gross sales ($ millions), the number of theaters the movie was shown in, and the number of weeks the movie was in release are common variables used to measure the success of a movie. Data on the top 100 grossing movies released in 2016 (Box Office Mojo website) are contained in the attached Excel file. We will use the numerical methods of descriptive statistics discussed in Chapter 3 to create a report of our findings.

1. Find descriptive statistics, including the mean, median, mode, range, standard deviation, and quartiles, for each of the four variables described above. Discuss what the statistics you find tell us about the movie industry.

2. According to Total Gross Sales, what movies if any, should be considered high-performance outliers? Explain how you arrived at your answer mathematically. (Use the method on p. 134 for detecting outliers.) Round any calculations/data to two decimal values.

3. Compute descriptive statistics showing the relationship between total gross sales and each of the other variables. These need to include the covariance and correlation coefficient. Discuss the relationships.

Movie Title	Opening Gross Sales ($ millions)	Total Gross Sales ($ millions)	Number of Theaters	Weeks in Release
Rogue One: A Star Wars Story	155.08	532.18	4,157	20
Finding Dory	135.06	486.30	4,305	25
Captain America: Civil War	179.14	408.08	4,226	20
The Secret Life of Pets	104.35	368.38	4,381	25
The Jungle Book (2016)	103.26	364.00	4,144	24
Deadpool	132.43	363.07	3,856	18
Zootopia	75.06	341.27	3,959	22
Batman v Superman: Dawn of Justice	166.01	330.36	4,256	12
Suicide Squad	133.68	325.10	4,255	14
Sing	35.26	270.40	4,029	20
Moana	56.63	248.76	3,875	22
Fantastic Beasts and Where To Find Them	74.40	234.04	4,144	19
Doctor Strange	85.06	232.64	3,882	19
Hidden Figures	0.52	169.61	3,416	46
Jason Bourne	59.22	162.43	4,039	21
Star Trek Beyond	59.25	158.85	3,928	13
X-Men: Apocalypse	65.77	155.44	4,153	9
Trolls	46.58	153.71	4,066	21
La La Land	0.88	151.10	3,236	20
Kung Fu Panda 3	41.28	143.53	3,987	25
Ghostbusters (2016)	46.02	128.35	3,963	17
Central Intelligence	35.54	127.44	3,508	11
The Legend of Tarzan	38.53	126.64	3,591	11
Sully	35.03	125.07	3,955	20
Bad Moms	23.82	113.26	3,215	13
The Angry Birds Movie	38.16	107.51	3,932	17
Independence Day: Resurgence	41.04	103.14	4,130	12
The Conjuring 2	40.41	102.47	3,356	11
Arrival	24.07	100.55	3,115	17
Passengers (2016)	14.87	100.01	3,478	17
Sausage Party	34.26	97.69	3,135	19
The Magnificent Seven (2016)	34.70	93.43	3,696	15
Ride Along 2	35.24	91.22	3,192	22
Don't Breathe	26.41	89.22	3,384	17
Miss Peregrine's Home for Peculiar Children	28.87	87.24	3,835	19
The Accountant	24.71	86.26	3,402	13
Teenage Mutant Ninja Turtles: Out of the Shadows	35.32	82.05	4,071	14
The Purge: Election Year	31.52	79.21	2,821	15
Alice Through the Looking Glass	26.86	77.04	3,763	14
Pete's Dragon (2016)	21.51	76.23	3,702	18
The Girl on the Train (2016)	24.54	75.40	3,241	12
Boo! A Madea Halloween	28.50	73.21	2,299	9
Storks	21.31	72.68	3,922	16
10 Cloverfield Lane	24.73	72.08	3,427	12
Lights Out	21.69	67.27	2,835	10
Hacksaw Ridge	15.19	67.21	2,971	18
The Divergent Series: Allegiant	29.03	66.18	3,740	11
Now You See Me 2	22.38	65.08	3,232	11
Ice Age: Collision Course	21.37	64.06	3,997	15
The Boss	23.59	63.29	3,495	17
London Has Fallen	21.64	62.68	3,492	13
Miracles from Heaven	14.81	61.71	3,155	18
Deepwater Horizon	20.22	61.43	3,403	11
Why Him?	11.00	60.32	3,008	13
My Big Fat Greek Wedding 2	17.86	59.69	3,179	9
Jack Reacher: Never Go Back	22.87	58.70	3,780	12
Fences	0.13	57.68	2,368	15
Me Before You	18.72	56.25	2,762	11
The BFG	18.78	55.48	3,392	15
Neighbors 2: Sorority Rising	21.76	55.46	3,416	8
The Shallows	16.80	55.12	2,962	14
Office Christmas Party	16.89	54.77	3,210	7
Assassin's Creed	10.28	54.65	2,996	11
Barbershop: The Next Cut	20.24	54.03	2,676	13
13 Hours: The Secret Soldiers of Benghazi	16.19	52.85	2,917	10
Lion	0.12	51.74	1,802	24
The Huntsman: Winter's War	19.45	48.39	3,802	15
Kubo and the Two Strings	12.61	48.02	3,279	15
Manchester by the Sea	0.26	47.70	1,213	23
Warcraft	24.17	47.37	3,406	13
How to Be Single	17.88	46.84	3,357	9
Mike and Dave Need Wedding Dates	16.63	46.01	3,008	14
War Dogs	14.69	43.03	3,258	9
Almost Christmas	15.13	42.16	2,379	9
Money Monster	14.79	41.01	3,104	12
Allied	12.70	40.10	3,160	9
Nerve	9.45	38.58	2,538	10
Risen	11.80	36.88	2,915	13
The Nice Guys	11.20	36.26	2,865	11
The Boy (2016)	10.78	35.82	2,671	10
Dirty Grandpa	11.11	35.59	2,912	8
Ouija: Origin of Evil	14.07	35.14	3,168	10
The 5th Wave	10.33	34.92	2,908	18
Inferno	14.86	34.34	3,576	12
Mother's Day	8.37	32.49	3,291	7
Patriots Day	0.16	31.89	3,120	11
Gods of Egypt	14.12	31.15	3,117	11
Collateral Beauty	7.10	31.02	3,028	8
Hail, Caesar!	11.36	30.50	2,248	21
When the Bough Breaks	14.20	29.75	2,246	10
Zoolander 2	13.84	28.85	3,418	7
Moonlight (2016)	0.40	27.85	1,564	28
The Finest Hours	10.29	27.57	3,143	10
Florence Foster Jenkins	6.60	27.38	1,528	11
Hell or High Water	0.62	27.01	1,505	14
The Forest	12.74	26.59	2,509	10
Ben-Hur (2016)	11.20	26.41	3,084	7
The Witch	8.80	25.14	2,204	14
Bridget Jones's Baby	8.57	24.25	2,930	13
Kevin Hart: What Now?	11.77	23.59	2,567	9

Answer 1

Find descriptive statistics, including the mean, median, mode, range, standard deviation, and quartiles, for each of the four variables described above. Discuss what the statistics you find tell us about the movie industry.

	Opening Gross Sales ($ millions)	Total Gross Sales ($ millions)	Number of Theaters	Weeks in Release
count	100	100	100	100
mean	32.0850	103.8190	3,282.36	14.73
sample standard deviation	36.3484	105.5382	668.29	5.82
sample variance	1,321.2085	11,138.3096	4,46,611.75	33.86
minimum	0.12	23.59	1213	7
maximum	179.14	532.18	4381	46
range	179.02	508.59	3168	39
1st quartile	12.4075	40.7825	2,954.00	11.00
median	20.7750	62.9850	3,285.00	13.00
3rd quartile	35.2450	108.9475	3,840.25	18.00
interquartile range	22.8375	68.1650	886.25	7.00
mode	11.2000	#N/A	4,144.00	11.00

The statistics tell us that the total sales of movies is good success in the movie industry.

According to Total Gross Sales, what movies if any, should be considered high-performance outliers? Explain how you arrived at your answer mathematically. (Use the method on p. 134 for detecting outliers.) Round any calculations/data to two decimal values.

	Opening Gross Sales ($ millions)	Total Gross Sales ($ millions)	Number of Theaters	Weeks in Release
count	100	100	100	100
low extremes	0	0	0	0
low outliers	0	0	4	0
high outliers	4	4	0	0
high extremes	7	9	0	1

There is a total of 17 high-performance outliers.

Compute descriptive statistics showing the relationship between total gross sales and each of the other variables. These need to include the covariance and correlation coefficient. Discuss the relationships.

	Covariance	Correlation coefficient
Total Gross Sales & Opening Gross Sales	3520.66	0.917759
Total Gross Sales & Number of Theaters	43265.34	0.613431
Total Gross Sales & Weeks in Release	290.8391	0.473617

There is a strong positive relationship between Total Gross Sales & Opening Gross Sales.

There is a moderate positive relationship between Total Gross Sales & Number of Theaters.

There is a moderate positive relationship between Total Gross Sales & Weeks in Release.