Questions and Answers
When constructing a frequency distribution, the class width should be an even number.
False
The lower class limit represents the smallest data value that can be included in the class.
True
A group frequency distribution is used when the range of the data values is relatively small.
False
If the limits for a class were 20-38, the boundaries would be 19.5-38.5.
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For the class 16.3-28.8, the width is 7.
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An ogive graph is also called a cumulative frequency graph.
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The cumulative frequency polygon is the sum of the frequencies accumulated to the upper boundary of a class in the distribution.
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A frequency polygon and a histogram have the same overall shape.
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An ogive and a frequency polygon have the same overall shape.
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The frequency polygon is a graph that displays the data by using lines that connect points plotted for the frequencies at the midpoints of the classes.
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A histogram uses the midpoints for the x values and the frequencies as the y values.
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A histogram is a graph that represents the cumulative frequencies for the classes in a frequency distribution.
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A Pareto chart is useful for showing percentages of the total.
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A stem and leaf plot is useful for keeping more precision than a grouped frequency distribution.
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Graphs give a visual representation that enables readers to analyze and interpret data more easily than they could simply by looking at numbers.
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A time series graph represents data that occur over a specific period.
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On a Pareto chart, the frequencies are arranged from lowest to highest.
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A pie graph is useful to show the trend of the data over time.
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A time series graph is useful for representing the frequencies of data categories over a period of several years.
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A time series graph is useful for detecting long-term trends over a period of time.
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A Pareto chart arranges data from largest to smallest according to frequencies.
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When two sets of data are compared on the same graph using two lines, it is called a compound time series graph.
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A pie graph would best represent the number of inches of rain that has fallen in Ohio each day for the past 2 months.
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A pie graph was created showing the number of children per family. If 234 families were in the survey and the section depicting families with three children represented 120 degrees, the number of families with three children was 78.
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When data are collected in original form they are called?
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The _____ is the number of values in a specific class of distribution.
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If a frequency distribution had class boundaries of 132.5-147.5, what would be the class width?
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For class 7-19, the upper class limit is?
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What are the boundaries of the class 3-15?
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What would be the boundaries on the average age for high school graduates if they were reported to be 18 years old?
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What is the midpoint of the class 4-16?
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Greg wants to construct a frequency distribution for the political affiliation of the employees at Owen's Hardware Store. What type of distribution should he use?
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What is the lower class limit in the class 13-17?
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What is the midpoint of the classes 13.5-17?
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Using the class 23-35, what is the upper class boundary?
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The _____ is obtained by first adding the lower and upper limits and then dividing by 2.
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What is the lower class limit in the class -6 to 9?
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The range 32.17 - 34.63 is not a good choice for class boundaries because _______.
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Thirty students recorded the colors of their eyes, choosing from the colors brown, blue, green, hazel, and black. This data can be appropriately summarized in a?
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What are the boundaries of the class 1.87-3.43?
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When the range is large and classes that are several units in width are needed, a __________ frequency distribution is used.
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The three most commonly used graphs in research are the histogram, the _____, and the cumulative frequency graph (ogive).
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The graphs that have their distribution as proportions instead of raw data frequencies are called ______.
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Which type of graph represents the data by using vertical bars of various heights to indicate frequencies?
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If data is clustered at one end or the other, it indicates that there is a __________.
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A weatherman records the amount of rain that has fallen in Portland, Oregon during each day. What type of graph should he use?
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Pareto charts have units that are used for frequency that are ____ in size.
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An automobile dealer wants to construct a pie graph to represent types of cars sold in July. He sold 72 cars; 16 of which were convertibles. The convertibles will represent how many degrees in the circle?
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In a pie graph, if pepperoni pizza were 24/72 of the distribution, how many degrees would be needed to represent pepperoni?
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Which graph should be used to represent the frequencies that certain types of classes are taken at Highlands Middle School?
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Exaggerating a one-dimensional increase by showing it in two dimensions is an example of a(n)
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The percentage of white, wheat, and rye bread sold at a supermarket each week is best shown using a ______ graph.
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A ______ would most appropriately represent the number of students that were enrolled in Statistics for the past ten years.
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Karen is constructing a pie graph to represent the number of hours her classmates do homework each day. She found that 8/24 did homework for three hours each day. In her pie graph, this would represent how many degrees?
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Study Notes
Frequency Distributions
- Class width does not need to be an even number.
- Lower class limit defines the smallest value of a class.
- Group frequency distribution is used for large data ranges, not small ones.
- Class boundaries are calculated as half a unit below the lower limit and half a unit above the upper limit.
Graphs and Representation
- An ogive graph is synonymous with a cumulative frequency graph.
- Cumulative frequency polygon sums frequencies up to the upper boundary of each class.
- Frequency polygons and histograms have similar shapes; however, they serve different purposes.
- A histogram shows raw frequency data, not cumulative.
- Pie charts are not ideal for showing trends; they represent parts of a whole.
Data Visualization Techniques
- Time series graphs depict data over a specified period.
- Pareto charts display frequencies from largest to smallest and emphasize significant factors.
- Categorical frequency distributions summarize data categorized by characteristic.
- Stem-and-leaf plots preserve precision over grouped frequency distributions.
Class Limits and Boundaries
- Class limits are crucial in defining frequency distributions.
- Class midpoint calculation involves averaging the lower and upper limits.
- Poorly chosen class boundaries, like range 32.17 - 34.63, can complicate interpretations.
- The upper class limit is the highest value in a class, while the lower class limit is the lowest.
Graph Types and Uses
- Histograms represent frequency distributions using vertical bars.
- Relative frequency graphs show proportions rather than raw data.
- Time series graphs fit longitudinal data and detect trends over time.
- Misleading graphs can exaggerate data representation, distorting perceptions.
Frequency Calculations and Examples
- When comparing data, a compound time series graph uses two lines.
- For a pie graph of types of bread sold, proportions are essential for accurate representation.
- Degrees in pie charts correlate to the frequency out of the total for accurate visual representation.
Usage of Graphs
- The correct type of graph enhances data clarity and comprehension.
- A Pareto chart is appropriate for class frequency representation at educational institutions.
- Time series graphs are suited for historical enrollment data in courses.
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Description
Explore the fundamentals of frequency distributions and graphical representations in statistics with this quiz. Learn about various graph types, their purposes, and techniques for effective data visualization. Perfect for students looking to reinforce their understanding of statistical concepts.
