Chapter 2.3, Problem 22E

Pass the popcorn: Following are the running times (in minutes) for the top 15 grossing movies of all time rated PG-13, and the top 15 grossing movies of all time rated R.

1. Construct back-to-back stem-and-leaf plots for these data sets.
2. Do the running times of R-rated movies differ greatly from the running times of movies rated PG or PG-13: or are they roughly similar?

To determine

To construct: A back-to-back slit stem-and-leaf plot for the data set.

Explanation of Solution

Given information:

The Following table represents the running times (in minutes) for the top 15 grossing movies

Movies Rated PG-13

Star Wars: The force Awakens	136
Avatar	162
Titanic	194
Jurassic Park	124
The Avengers	143
The Dark Knight	152
Avengers: Age of Ultron	141
The Dark Knight Rises	164
The Hunger Games: Catching Fire	146
Pirates of the Caribbean: Dead Man’s Chest	151
Iron Man 3	129
The Hunger Games	142
Captain Americs: Civil War	147
Spider-Man	121
Jurassic Park	127

Movies Rated R

The Passion of the Christ	126
Deadpool	106
American Sniper	132
The Matrix Reloaded	138
The Hangover	96
The Hangover Part II	102
Beverly Hills Cop	105
The Exorcist	122
Ted	106
Saving Private Ryan	170
300	117
Wedding Crashers	113
Terminator 2: Judgment Day	137
22 Jump Street	112
Gladiator	155

Definition used: Stem plot is a tool to visualize the shape of a distribution.

Calculation:

The back-to-back slit stem-and-leaf plot for the data set is given by

In the above back-to-back slit stem-and-leaf plot, Leaf 1 displays the lengths of time of the PG-13 movies and Leaf 2 does so for the R rated movies.

To determine

To explain: Whether the running times of R-rated movies differ greatly from the running times of movies rated PG or PG-13, or they roughly similar.

Explanation of Solution

Given information: Following are the running times (in minutes) for the top 15 grossing movies of all time rated PG-13, and the top 15 grossing movies of all time rated R.

Movies Rated PG-13

Star Wars: The force Awakens	136
Avatar	162
Titanic	194
Jurassic Park	124
The Avengers	143
The Dark Knight	152
Avengers: Age of Ultron	141
The Dark Knight Rises	164
The Hunger Games: Catching Fire	146
Pirates of the Caribbean: Dead Man’s Chest	151
Iron Man 3	129
The Hunger Games	142
Captain Americs: Civil War	147
Spider-Man	121
Jurassic Park	127

Movies Rated R

The Passion of the Christ	126
Deadpool	106
American Sniper	132
The Matrix Reloaded	138
The Hangover	96
The Hangover Part II	102
Beverly Hills Cop	105
The Exorcist	122
Ted	106
Saving Private Ryan	170
300	117
Wedding Crashers	113
Terminator 2: Judgment Day	137
22 Jump Street	112
Gladiator	155

The back-to-back slit stem-and-leaf plot for the data set is given by

From the above back-to-back slit stem-and-leaf plot, the R-rated movies tend to be shorter.

Therefore, they differ greatly.