RANDOM SAMPLING - SHOW ME THE MONEY!
INTRODUCTION
1.
Name your favorite movie of all time.
2. On average, how much money do you think a movie grosses (earns) in theaters?
3. Take a guess at the title of the top-grossing movie of 2013.
4. What do you think was the maximum amount grossed by a movie in 2013?
SAMPLING METHODS
5. Take a look at the list of the 200 top-grossing movies of 2013 and select 10 that you saw (or
wanted to see) in theaters. For purposes of this activity, we will consider these 200 movies
as a small population. In practice, populations are often much larger than 200 individuals,
sometimes reaching the hundreds of millions or more. Write the titles of those movies in
the table below, along with the amount they grossed in 2013. Notice that the listing of
movies gives the gross income rounded to the nearest tenth of a million, so that a movie
listed as earning $191.5 really grossed $191,500,000. The order in which you write the
movies in the table below does not matter.
Movie Title
WSS: Stats Ed as Part of CCSS
Gross Income (Millions)
Doug Tyson
[email protected]
6. Compute and record the mean gross income for the 10 movies you selected. This number
is called the sample mean.
7. Is your sample mean the same as all the other sample means computed by the other
students in your class?
It’s probably not surprising to you that your sample mean differs from those of other students
because you have most likely chosen different samples. The fact that different samples yield
different statistics (in this case different sample means) is called sampling variability.
8. Combine your results with those of your classmates by creating a dotplot of sample means
on the board. Then, record this dotplot on the number line below, carefully labeling the
axis.
9. Based on the previous dotplot, without any calculations, what do you suppose the mean
gross income for the population of all 200 movies might be?
The method you used to take samples from the population is based on your experience and
interest in movies. It turns out that this is not a particularly good way to sample if you wish to
generate samples that are representative (good images) of the population. Instead of using human
experience, judgment, or interest to choose samples, statisticians use chance to select samples
from large populations. Samples selected by a chance process are called random samples.
WSS: Stats Ed as Part of CCSS
Doug Tyson
[email protected]
10. Your instructor will give you instructions on how to use random chance to select 10 movies
from the population of 200 movies. You will draw chips from a container, use a table of
random digits, or use technology to generate 10 random numbers from 1-200. Find the ID
numbers in the table below that match your randomly chosen numbers. Record the ID
number, title of the movie, and gross income in the following table.
ID
Number
Movie Title
Gross Income
(Millions)
11. Compute and record the mean gross income for the 10 movies you selected. This number
is called the sample mean, but this time the sample mean has been generated by a random
sample. Is your sample mean the same as all the other sample means computed by the
other students in your class?
12. Combine your results with those of your classmates by creating a dotplot of sample means
on the board. Then, record this dotplot on the number line below, carefully labeling the
axis.
WSS: Stats Ed as Part of CCSS
Doug Tyson
[email protected]
13. Based on the previous dotplot, without any calculations, what do you suppose the mean
gross income for the population of all 200 movies might be?
14. Is your guess for the mean gross income from a random sample somewhat different from
your guess when you chose your own sample?
15. The population’s mean gross income for the population of all 200 movies is $54.4 million.
Go back to your dotplots in #8 and #12 and draw a vertical line on your number line at
54.4. Did the sample means from you and your classmates do a pretty good job of
estimating the population mean when you chose your sample by thinking of movies you
saw or wished to see? How about when you obtained your samples through chance? What
have you learned about the use of random samples from populations?
16. With enough time, you and your classmates could continue drawing random samples of 10
movies, computing the sample mean for each sample, and building the dotplot in #12
above. In order to save time, your instructor will show you a simulation of this process
using Fathom software. When the simulation is finished, create a rough sketch of the
resulting dotplot below. Label the horizontal axis and draw two vertical lines: one at the
center of all the dots and one at the population mean.
It should be clear that rather than producing haphazard results, random
sampling actually follows regular patterns that can be predicted with
advanced mathematics and statistics. These patterns can then be used
to make inferences (conclusions) about the population from random
samples.
WSS: Stats Ed as Part of CCSS
Doug Tyson
[email protected]
ID
001
002
003
004
005
006
007
008
009
010
011
012
013
014
015
016
017
018
019
020
021
022
023
024
025
026
027
028
029
030
031
032
033
034
035
036
037
038
039
040
041
042
043
044
045
046
047
048
049
050
Movie Title
The Hunger Games: Catching Fire
Iron Man 3
Frozen
Despicable Me 2
Man of Steel
Gravity
Monsters University
The Hobbit: The Desolation of Smaug
Fast & Furious 6
Oz The Great and Powerful
Star Trek Into Darkness
Thor: The Dark World
World War Z
The Croods
The Heat
We're the Millers
American Hustle
The Great Gatsby (2013)
The Conjuring
Identity Thief
Grown Ups 2
The Wolverine
Anchorman 2: The Legend Continues
Lone Survivor
G.I. Joe: Retaliation
Cloudy with a Chance of Meatballs 2
Now You See Me
The Wolf of Wall Street
Lee Daniels' The Butler
The Hangover Part III
Epic
Captain Phillips
Jackass Presents: Bad Grandpa
Pacific Rim
This is the End
Olympus Has Fallen
42
Elysium
Planes
The Lone Ranger
Oblivion
Insidious Chapter 2
Saving Mr. Banks
Turbo
2 Guns
White House Down
Mama
Safe Haven
The Smurfs 2
The Best Man Holiday
WSS: Stats Ed as Part of CCSS
Total
Gross
(Millions)
424.7
409.0
400.7
368.1
291.0
274.1
268.5
258.4
238.7
234.9
228.8
206.4
202.4
187.2
159.6
150.4
150.1
144.8
137.4
134.5
133.7
132.6
125.2
125.1
122.5
119.8
117.7
116.9
116.6
112.2
107.5
107.1
102.0
101.8
101.5
98.9
95.0
93.1
90.3
89.3
89.1
83.6
83.3
83.0
75.6
73.1
71.6
71.3
71.0
70.5
Doug Tyson
ID
051
052
053
054
055
056
057
058
059
060
061
062
063
064
065
066
067
068
069
070
071
072
073
074
075
076
077
078
079
080
081
082
083
084
085
086
087
088
089
090
091
092
093
094
095
096
097
098
099
100
Total
Gross
(Millions)
Movie Title
Percy Jackson: Sea of Monsters
A Good Day to Die Hard
Warm Bodies
Jack the Giant Slayer
The Purge
Last Vegas
Ender's Game
Prisoners
After Earth
The Secret Life of Walter Mitty
Escape From Planet Earth
12 Years a Slave
Free Birds
Hansel and Gretel: Witch Hunters
Evil Dead (2013)
Red 2
Tyler Perry's A Madea Christmas
Tyler Perry's Temptation: Confessions of a
Marriage Counselor
The Call
Pain and Gain
Gangster Squad
Jurassic Park 3D
The Internship
Instructions Not Included
Snitch
Riddick
A Haunted House
47 Ronin
August: Osage County
Philomena
The Family (2013)
Walking with Dinosaurs
Carrie (2013)
Texas Chainsaw 3D
R.I.P.D.
Blue Jasmine
Kevin Hart: Let Me Explain
Side Effects (2013)
Scary Movie 5
The Mortal Instruments: City of Bones
Delivery Man
Grudge Match
One Direction: This is Us
Kick-Ass 2
Dallas Buyers Club
Rush (2013)
The Host (2013)
The World's End
21 and Over
Her (2013)
68.6
67.3
66.4
65.2
64.5
63.9
61.7
61.0
60.5
58.2
57.0
56.7
55.8
55.7
54.2
53.3
52.5
52.0
51.9
49.9
46.0
45.4
44.7
44.5
42.9
42.0
40.0
38.4
37.7
37.7
36.9
36.1
35.3
34.3
33.6
33.4
32.2
32.2
32.0
31.2
30.7
29.8
28.9
28.8
27.3
26.9
26.6
26.0
25.7
25.6
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ID
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
Movie Title
Escape Plan
Don Jon
The Incredible Burt Wonderstone
The Big Wedding
Mud
Baggage Claim
The Way, Way Back
The Book Thief
The Place Beyond the Pines
Homefront
Broken City
Beautiful Creatures (2013)
Runner Runner
You're Next
Quartet
Admission
Nebraska
Parker
Enough Said
Dark Skies
The Counselor
Jobs
Fruitvale Station
About Time
The Last Exorcism Part II
Spring Breakers
Inside Llewyn Davis
The Last Stand
Out of the Furnace
Dead Man Down
Getaway (2013)
Bullet to the Head
Tyler Perry Presents Peeples
Battle of the Year
Movie 43
Mandela: Long Walk to Freedom
Before Midnight
Dhoom 3
Machete Kills
Paranoia
Black Nativity
The Spectacular Now
The Grandmaster
All Is Lost
Believe
The Bling Ring
Pulling Strings
Closed Circuit
The Wizard of Oz (3D/IMAX)
Chennai Express
WSS: Stats Ed as Part of CCSS
Total
Gross
(Millions)
25.1
24.5
22.5
21.8
21.6
21.6
21.5
21.5
21.4
20.2
19.7
19.5
19.3
18.5
18.4
18.0
17.7
17.6
17.6
17.4
17.0
16.1
16.1
15.3
15.2
14.1
13.2
12.1
11.3
10.9
10.5
9.5
9.2
8.9
8.8
8.3
8.1
8.0
8.0
7.4
7.0
6.9
6.6
6.3
6.2
5.8
5.8
5.8
5.6
5.3
Doug Tyson
ID
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
Total
Gross
(Millions)
Movie Title
The Company You Keep
20 Feet from Stardom
Jerusalem
Much Ado About Nothing (2013)
Frances Ha
Yeh Jawaani Hai Deewani
The To-Do List
Metallica Through the Never
Emperor
Journey to the South Pacific
Stand Up Guys
The Fifth Estate
Top Gun 3D
In a World
Home Run
The Great Beauty
Filly Brown
Ram-Leela
Grace Unplugged
The Sapphires
The Gatekeepers
I'm In Love With a Church Girl
No (2013)
Trance
The East
Renoir
The Christmas Candle
Blue Is the Warmest Color
Oldboy (2013)
Krrish 3
Austenland
The Saratov Approach
2013 Oscar Nominated Short Films
Blackfish
The Iceman (2013)
Fill the Void
Girl Rising
The Attack
Stoker
Unfinished Song
Bhaag Milkha Bhaag
Love is All You Need
Stories We Tell
Race 2
Bless Me Ultima
Kon-Tiki
Disconnect
Girl Most Likely
I'm So Excited
Wadjda (U.S. only)
5.1
4.9
4.6
4.3
4.1
3.8
3.5
3.4
3.3
3.3
3.3
3.3
3.0
3.0
2.9
2.9
2.9
2.7
2.5
2.5
2.4
2.4
2.3
2.3
2.3
2.3
2.3
2.2
2.2
2.2
2.2
2.1
2.1
2.1
2.0
1.8
1.7
1.7
1.7
1.7
1.6
1.6
1.6
1.6
1.6
1.5
1.4
1.4
1.4
1.3
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