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Ch. 2 - Exploring Data with Tables and Graphs
Triola - Elementary Statistics 14th Edition
Triola14th EditionElementary StatisticsISBN: 9780137366446Not the one you use?Change textbook
Chapter 2, Problem 2.1.25

In Exercises 25 and 26, construct the cumulative frequency distribution that corresponds to the frequency distribution in the exercise indicated.


Exercise 5 (Age of Best Actress When Oscar Was Won)
Table showing the age distribution of Best Actress winners at the time of their Oscar win, with corresponding frequencies.

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Identify the frequency distribution from the table. The age groups and their corresponding frequencies are: 20-29 (31), 30-39 (34), 40-49 (15), 50-59 (3), 60-69 (6), 70-79 (1), and 80-89 (1).
Start constructing the cumulative frequency distribution by taking the first frequency as it is. For the age group 20-29, the cumulative frequency is 31.
Add the frequency of the next age group to the cumulative frequency of the previous group. For the age group 30-39, add 34 to the previous cumulative frequency of 31, resulting in a cumulative frequency of 65.
Continue this process for each subsequent age group. For the age group 40-49, add 15 to the previous cumulative frequency of 65, resulting in a cumulative frequency of 80.
Repeat the addition for all remaining age groups: 50-59 (add 3 to 80), 60-69 (add 6 to the result), 70-79 (add 1), and 80-89 (add 1). This will give you the complete cumulative frequency distribution.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Frequency Distribution

A frequency distribution is a summary of data that shows the number of occurrences of each value or range of values in a dataset. In the context of the table, it displays how many Best Actress winners fall into each age group when they won an Oscar. This helps in understanding the distribution and concentration of ages among the winners.
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Intro to Frequency Distributions

Cumulative Frequency

Cumulative frequency is the running total of frequencies through the classes in a frequency distribution. It shows the number of observations below a particular value or class interval. To construct a cumulative frequency distribution, you add the frequency of each class interval to the sum of the frequencies of all preceding intervals, providing insight into the accumulation of data points.
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Intro to Frequency Distributions

Age Group Analysis

Age group analysis involves examining the distribution of data across different age ranges to identify patterns or trends. In this exercise, analyzing the age groups of Best Actress winners can reveal insights into the typical age range for winning an Oscar, highlighting any age-related trends or anomalies in the data. This analysis is crucial for understanding demographic patterns in award-winning.
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Step 1: Write Hypotheses
Related Practice
Textbook Question

Causation A study has shown that there is a correlation between body weight and blood pressure. Higher body weights are associated with higher blood pressure levels. Can we conclude that gaining weight is a cause of increased blood pressure?

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Textbook Question

In Exercises 9–18, construct the histograms and answer the given questions.


Burger King Dinner Service Times Use the frequency distribution from Exercise 18 in Section 2-1 to construct a histogram. Using a strict interpretation of the criteria for being a normal distribution, does the histogram appear to depict data from a population with a normal distribution?

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Textbook Question

In Exercises 11 and 12 construct the Pareto chart.


Box Office Boffo Recent annual gross revenue (millions of dollars) for the leading movie studios are as follows: 20th Century Fox (1082), Buena Vista (3092), Paramount (757), Sony/Columbia (1304), Universal (1772), Warner Brothers (1941). Are these data likely to be reasonably accurate?

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Textbook Question

Presidents Listed below are the ages (years) of presidents of the United States at the times of their first inaugurations (from Data Set 22 “Presidents” in Appendix B). Presidents who took office as a result of an assassination or resignation are not included. The data are current as of this writing. Use these ages to construct a frequency distribution. Use a class width of 5 years and begin with a lower class limit of 40 years. Do the ages appear to have a normal distribution?

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Textbook Question

In Exercises 5–8, answer the questions by referring to the following Minitab-generated histogram, which depicts the weights (grams) of all quarters listed in Data Set 40 “Coin Weights” in Appendix B. (Grams are actually units of mass and the values shown on the horizontal scale are rounded.)

Class Width and Class Limits Give the approximate values of the class width, and the lower and upper class limits of the class depicted in the bar farthest to the left.

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Textbook Question

In Exercises 5–8, answer the questions by referring to the following Minitab-generated histogram, which depicts the weights (grams) of all quarters listed in Data Set 40 “Coin Weights” in Appendix B. (Grams are actually units of mass and the values shown on the horizontal scale are rounded.)


Relative Frequency Histogram How would the shape of the histogram change if the vertical scale uses relative frequencies expressed in percentages instead of the actual frequency counts as shown here?

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