Question

The article "Tobacco and Alcohol Use in G-Rated Children's Animated Films" (Journal of the American Medical Association [1999]: \(1131-1136\) ) reported exposure to tobacco and alcohol use in all G-rated animated films released between 1937 and 1997 by five major film studios. The researchers found that tobacco use was shown in \(56 \%\) of the reviewed films. Data on the total tobacco exposure time (in seconds) for films with tobacco use produced by Walt Disney, Inc., were as follows: $$ \begin{array}{rrrrrrrrrr} 223 & 176 & 548 & 37 & 158 & 51 & 299 & 37 & 11 & 165 \\ 74 & 92 & 6 & 23 & 206 & 9 & & & & \end{array} $$ Data for \(11 \mathrm{G}\) -rated animated films showing tobacco use that were produced by MGM/United Artists, Warner Brothers, Universal, and Twentieth Century Fox were also given. The tobacco exposure times (in seconds) for these films was as follows: $$ \begin{array}{lllllllllll} 205 & 162 & 6 & 1 & 117 & 5 & 91 & 155 & 24 & 55 & 17 \end{array} $$ Construct a comparative stem-and-leaf display for these data. Comment on the interesting features of this display.

Short answer

A stem-and-leaf display will let us see the distribution of the exposure times in the films of the given animation studios. It gives us a quick snapshot of the data, letting us see where the majority of the numbers fall, and if there are any outliers. Some key features to discuss include spread and center of the data, and whether the data is symmetric or skewed.

Step-by-step solution

Prepare the Data

To start, sort the data in ascending order. For the Disney set, it will look like: 6, 9, 11, 23, 37, 37, 51, 74, 92, 158, 165, 176, 206, 223, 299 and 548. For the other studios set, it will look like: 1, 5, 6, 17, 24, 55, 91, 117, 155, 162, and 205.

Construct the Stem-and-Leaf Display

Divide each observed value into two parts, a stem (the first digit or digits) and a leaf (the final digit). For this exercise, since all the values are less than 1000, let's take the first one or two digits as stem and the last digit as leaf. Construct two columns: one for Walt Disney Inc. and the other for the collective studios. Then start constructing the stem-and-leaf diagram side by side. For example, if the leaf is 6 and its stem is 0 for Disney dataset, then in the same row, we must check if there is any comparable stem-and-leaf combination in the second group of studios.

Discuss the Features

After creating the comparative stem-and-leaf display, the key features of this display need to be discussed. This may include discussion concerning the shape of the distribution, center, spread, outliers and any other unusual features or prominent comparison points between the two data sets.