Questions and Answers
Which of the following does not need to be done when constructing a frequency distribution? (Select one)
When data are collected in original form, they are called __________.
raw data
The ______ of a specific class is the number of data values contained in it.
frequency
If a frequency distribution had class boundaries of 132.5-147.5, what would be the class width?
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For the class 10-20, the upper class limit is?
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What are the boundaries of class 11-17?
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In an ungrouped frequency distribution of the average age of high school graduates, what would be the boundaries for the class of graduates who were reported to be 18 years old?
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What is the midpoint of the class 7-11?
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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 would be best?
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What is the lower class limit of the class 13-17?
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Which of the following pairs of class limits would be appropriate for grouping the numbers 13, 16, 11, and 18? (Select one)
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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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For the class 16.3-23.8, the width is 8.5.
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The cumulative frequency for a class is the sum of the frequencies of the classes less than and equal to the upper boundary of the specific class.
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An ogive is also called a cumulative frequency graph.
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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 frequency polygon and the histogram are two different ways to represent the same data set.
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For a given data set, the ogive and the frequency polygon will have the same overall shape.
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Graphs that show distribution using proportions instead of raw data as frequencies are called _______________ _____________ _________.
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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 midpoint of the classes.
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If the graph of a frequency distribution has a peak and the data tapers off more slowly to the right and more quickly to the left, the distribution is said to be ____________________.
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Study Notes
Frequency Distribution Basics
- Constructing a frequency distribution requires selecting the number of classes, ensuring classes are mutually exclusive, and finding the range; making the class width an even number is not necessary.
- Raw data refers to data collected in its original form without processing or categorization.
Class Definitions
- Frequency represents the count of data values in a specific class.
- The class width can be calculated from class boundaries; for example, the boundaries 132.5-147.5 yield a width of 15.
- Upper class limits and lower class limits define the ranges of classes; for the class 10-20, the upper limit is 20, and for 13-17, the lower limit is 13.
Class Boundaries and Midpoints
- Class boundaries account for the numbers that fall at the edges; for an 11-17 class, boundaries are 10.5 and 17.5.
- The midpoint of the class 7-11 is 9.
- For the average age of high school graduates reported as 18 years old, the boundaries are 17.5 - 18.5 years.
Types of Distributions
- Categorical frequency distributions are suitable for non-numeric data, such as political affiliation or eye colors (brown, blue, green, hazel, and black).
- A grouped frequency distribution is used when dealing with a large range that necessitates wider classes.
Cumulative Frequency and Ogives
- The cumulative frequency for a class sums frequencies of all preceding classes, which can be visually represented in an ogive, also known as a cumulative frequency graph.
- An ogive and frequency polygon represent the same data differently; they do not share the same overall shape.
Graphing Frequency Data
- Common types of graphs in research include histograms, frequency polygons, and cumulative frequency graphs (ogives).
- Frequency polygons connect points plotted for class midpoints while illustrating the data trends in a visual format.
- Relative frequency graphs illustrate distributions using proportions instead of raw data frequencies.
Distribution Shapes
- If a frequency distribution graph peaks and tapers off more slowly to the right and more quickly to the left, it is classified as right-skewed.
- The distinct shapes of ogives and frequency polygons reflect differences in data representation, despite both being based on the same data set.
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Test your knowledge of key statistics concepts with these flashcards. Each card focuses on crucial aspects of creating frequency distributions and understanding data terminology. This quiz is perfect for reinforcing your understanding of statistics.
