/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 6 Do running times of American mov... [FREE SOLUTION] | 91Ó°ÊÓ

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Do running times of American movies differ somehow from running times of French movies? The author investigated this question by randomly selecting 25 recent movies of each type, resulting in the following running times: Am: \(94 \quad 90 \quad 95 \quad 93 \quad 128 \quad 95 \quad 125 \quad 91 \quad 104\) \(\begin{array}{llllllllllll}110 & 92 & 113 & 116 & 90 & 97 & 103 & 95 & 120 & 109 & 91 & 138\end{array}\) Fr: \(123116 \quad 90 \quad 158 \quad 12211912590 \quad 96 \quad 94\) \(\begin{array}{llllllllllll}106 & 95 & 125 & 122 & 103 & 96 & 111 & 81 & 113 & 128 & 93 & 92\end{array}\) Construct a comparative stem-and-leaf display by listing stems in the middle of your paper and then placing the Am leaves out to the left and the Fr leaves out to the right. Then comment on interesting features of the display.

Short Answer

Expert verified
The plot shows American movies are generally shorter than French movies.

Step by step solution

01

Organize Data into Stems

Divide the running times into stems by determining the tens digit for each time. For example, the stem for 90 is 9, and for 104, it is 10. Do this for both American and French movies.
02

Create a Stem-and-Leaf Plot

List stems in a column. To the left of each stem, list the leaves for American movie running times (ones digit) and to the right, list the leaves for French movie running times. Each leaf corresponds to the ones digit of a running time.
03

Fill in the American Movie Leaves

For each stem, place the ones digit from American movie running times in increasing order on the left side of the stem. Continue this process for all stems.
04

Fill in the French Movie Leaves

For each stem, place the ones digit from French movie running times in increasing order on the right side of the stem. Continue this process for all stems.
05

Analyze the Stem-and-Leaf Plot

Examine the completed stem-and-leaf plot to discern patterns or differences between American and French movie running times. Notable points might include the spread and clustering of data or any outliers.

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Key Concepts

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

Comparative Data Analysis
Comparative data analysis is the method of comparing datasets to identify patterns or differences. Understanding these differences is a key aspect of data analysis. By organizing data visually, such as using a stem-and-leaf plot, we can easily see how two sets of data compare.

In this exercise, we're comparing running times of American and French movies. The stem-and-leaf plot serves as our visual tool. By splitting the data based on decades, known as stems (tens digit), we see how running times are distributed within each decade.

Studying the structure of each dataset can reveal which movies typically have longer or shorter running times. This method highlights both similarities and distinctions between datasets. It is crucial in identifying patterns, such as whether one group of movies tends to have longer durations than the other. This comparative analysis allows us to make informed conclusions and evaluations.
Descriptive Statistics
Descriptive statistics provide a way to summarize and organize data in an understandable way. With tools like stem-and-leaf plots, we can see data distributions at a glance.

For this analysis, each stem represents a "bin" or category, while the leaves show the exact data points. This method not only allows for quick visual representation but also retains actual data points. This can be invaluable for understanding both central tendencies and variations around a data set.

A stem-and-leaf plot gives insights into the range, central tendency, and variability. In simple terms, it helps to see where most data points cluster and whether there are any outliers or unique points that stand out from the rest. This is vital when trying to explain differences or similarities in the datasets, such as understanding the typical movie running time.
Movie Running Times Comparison
When comparing movie running times using a stem-and-leaf plot, several interesting features can emerge. The plot shows if one group of movies has consistently longer or shorter running times.

Upon examining the running times of American and French movies, look for clusters, spread, and any outliers. Clustering indicates where most movies fall in terms of length. Spread gives us an idea of the range of movie durations in each dataset.

This comparison can point out noticeable features, such as whether American movies tend to be shorter or whether French movies have more variation in length. By physically separating the American and French movie data with a central stem, the comparison becomes clear and direct.
  • If clustering in one decade is visible, it suggests a common running time trend among the movies.

  • Important outliers can suggest unique trends or deviations that require further investigation.
  • Overall spread reveals the diversity in movie lengths, adding another layer for interpretation.
Through this method, a detailed narrative can be drawn from the data, allowing conclusions about typical running times and any peculiar differences between the movie groups.

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Most popular questions from this chapter

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