91Ó°ÊÓ

'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: \(\begin{array}{llllllllll}223 & 176 & 548 & 37 & 158 & 51 & 299 & 37 & 11 & 165\end{array}\) \(\begin{array}{ll}74 & 92\end{array}\) \(23206 \quad 9\) Data for 11 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.

Step by step solution

01

Organize data

Organize the data for both Walt Disney films and the films from the other companies in increasing order. Walt Disney: \[ 9, 11, 37, 37, 51, 74, 92, 158, 165, 176, 223, 232, 299, 548 \]. Other companies: \[ 1, 5, 6, 17, 24, 55, 91, 117, 155, 162, 205 \]

02

Determine the stems and leaves

Each stem represents tens place of the numbers and leaves represents units place. For both Disney and other companies, since the data ranges from single digits to hundreds, the stems will range from 0 to 50. The leaves are the actual data values.

03

Draw the stem-and-leaf plot

Now, the stems must be written in a column with small values at top and working downwards to higher values. Then, the corresponding leaves for each stem in data are written. The resulting plot can be read as normal numbers, combining stem and leaf.

04

Interpretation

Compare the spread, center, and shape of distribution for both sets of data. Look for outliers or any other notable features of the comparative display. An important feature to note may be any stark differences in tobacco exposure time between the two groups of film producers. For Disney, there are several films with shorter and several with much longer exposure times. For the other companies, the majority of films have quite short exposure times.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Stem-and-Leaf Plot

A stem-and-leaf plot is a handy way to display quantitative data visually. It helps us to quickly see patterns and identify the frequency of different data points. The method organizes data by dividing each data point into a "stem" and a "leaf," hence the name.

The "stem" typically represents the leading digits or the highest order values in the data, while the "leaf" represents the unit place or the lower order values. For example, in the number 223, "22" would be the stem, and "3" would be the leaf. This separation is done for all data values, grouping them with common stems.

• It provides a clear overview of distribution.
• Easier comparison between datasets.
• Data points remain intact and visible.

To create a stem-and-leaf plot, first, sort the data. Organize by increasing order to make it simple. Assign stems and corresponding leaves for each dataset. Align the stems in a column, and arrange leaves to the right for each stem. This approach keeps the data structured and quickly readable, helping to spot any anomalies or outliers.

Comparative Analysis

A comparative analysis uses visual tools, like the stem-and-leaf plot, to compare two or more sets of data. This technique highlights differences, similarities, and trends between datasets.

In the context of the exercise, a comparative analysis examines tobacco exposure in Disney films versus other studios. Using a stem-and-leaf plot makes it easy to see how these two datasets differ in terms of exposure times.

• The "center" of a distribution is where most data points cluster, like the median or mean.
• An analysis also considers the "spread", indicating variability or range within data points.
• The "shape" shows the overall outline of data distribution, whether centered, skewed, or dispersed.

By analyzing these characteristics, students can discern patterns, such as longer exposure times in Disney films compared to generally shorter times in films from other studios. Ultimately, comparative analysis provides a deeper understanding of structured data relationships.

Descriptive Statistics

Descriptive statistics summarize or describe features and measures of a dataset. Primarily, it deals with central tendency, variability, and the distribution's shape.

In such a case as examining tobacco use in animated films, descriptive statistics might help unveil how typical exposure times differ between movie producers.

• Measures of central tendency include mean, median, and mode. These indicate where most data values lie.
• Measures of variability such as range, variance, and standard deviation show data spread and dispersion.
• Shape of distribution refers to the symmetry or asymmetry of data's graphical representation.

For Disney's tobacco exposure times, you might calculate the average and variance to communicate how frequently and widely spread the exposure is. Understanding descriptive statistics builds the foundation for identifying more complex statistical relationships and analyses in data sets.