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Ch. 2 - Descriptive Statistics
Larson - Elementary Statistics: Picturing the World 8th Edition
Larson8th EditionElementary Statistics: Picturing the WorldISBN: 9780137493470Non è quello che usi tu?Cambia libro di testo
Tutti i libri di testoLarson 8th EditionCh. 2 - Descriptive StatisticsProblema 2.4.1
Capitolo 2, Problema 2.4.1

Building Basic Skills and Vocabulary


Explain how to find the range of a data set. What is an advantage of using the range as a measure of variation? What is a disadvantage?

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To find the range of a data set, first identify the maximum value (the largest number) and the minimum value (the smallest number) in the data set.
Subtract the minimum value from the maximum value using the formula: Range=Maximum-Minimum.
An advantage of using the range as a measure of variation is that it is simple to calculate and provides a quick sense of the spread of the data.
A disadvantage of using the range is that it is highly sensitive to outliers, as it only considers the two extreme values and ignores the distribution of the rest of the data.
In summary, while the range is useful for a quick overview of variability, it may not provide a complete picture of the data's spread, especially in datasets with outliers or skewed distributions.

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Range

The range of a data set is a measure of variation that represents the difference between the maximum and minimum values in the set. To find the range, you simply subtract the smallest value from the largest value. This provides a quick sense of the spread of the data, indicating how far apart the values are.
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Advantages of Range

One advantage of using the range as a measure of variation is its simplicity and ease of calculation. It requires only two values (the maximum and minimum) and can be quickly computed, making it useful for a quick assessment of data spread. This straightforward approach can be particularly helpful in initial data analysis.
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Disadvantages of Range

A significant disadvantage of the range is that it is highly sensitive to outliers, which can skew the results. If the data set contains extreme values, the range may not accurately reflect the overall distribution of the data. This limitation makes it less reliable compared to other measures of variation, such as the interquartile range or standard deviation.
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Constructing a Frequency Distribution and a Relative Frequency Histogram In Exercises 37–40, construct a frequency distribution and a relative frequency histogram for the data set using five classes. Which class has the greatest relative frequency and which has the least relative frequency?

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Data set: Ratings from 1 (lowest) to 10 (highest) provided by 36 people after taste-testing a new flavor of protein bar 2 6 9 2 9 9 6 10 5 8 7 6 5 10 1 4 9 3 4 5 3 6 5 2 4 9 2 9 3 3 6 5 1 9 4 2

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Finding z-Scores The distribution of the ages of the winners of the Tour de France from 1903 to 2020 is approximately bell-shaped. The mean age is 27.9 years, with a standard deviation of 3.4 years. In Exercises 43–48, use the corresponding z-score to determine whether the age is unusual. Explain your reasoning. (Source: Le Tour de France)

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Building Basic Skills and Vocabulary


Given a data set, how do you know whether to calculate σ or s?

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use the frequency polygon to identify the class with the greatest, and the class with the least, frequency.

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In Exercises 37– 40, without performing any calculations, determine which measure of central tendency best represents the graphed data. Explain your reasoning.

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True or False? In Exercises 7–10, determine whether the statement is true or false. If it is false, rewrite it as a true statement.


The second quartile is the mean of an ordered data set.

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