A frequency distribution is the organization of raw data in table form, using classes and frequencies.
The frequency is the number of values in a specific class of the distribution.
The categorical frequency distribution is used for data that can be placed in specific categories, such as nominal or ordinal data.
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Birth Month - Data September May July October July August May May March September April August June July February January July January November April July March October December July October January December May March March February November April August July October February April June August August November July September December August July September October August December April September September June November November July July December November May August August December January September May
The class limits should have the decimal place value as the data, but the class boundaries should have one additional place value and end in a 5.
The class width is found by subtracting the lower ( or upper) class limit of one class from the lower ( or upper) class limit of the other class. The class width can also be found by subtracting the lower boundary from the upper boundary.
The class width cannot be found by subtracting the limits of a single class.
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Rules for Constructing a Frequency Distribution
There should be between 5 and 20 classes.
The class width should be an odd number. This ensures that the midpoint of each class has the same place value as the limits.
The class midpoint is obtained by adding the lower and upper boundaries and dividing by 2, or adding the lower and upper limits and dividing by 2.
The classes must be mutually exclusive.
The classes must be continuous. Do not omit classes with a frequency of zero unless they occur at the beginning or ending of the distribution.
Cumulative frequencies are used to show how many data values are accumulated up to and including a specific class.
When the range of data values is relatively small a frequency distribution can be constructed using single data values for each class. This type of distribution is called an ungrouped frequency distribution .
Example: The blood urea nitrogen (BUN) count of 20 randomly selected patients is given here in milligrams per deciliter. Construct an ungrouped frequency distribution for the data.
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Reasons For Constructing a Frequency Distribution
To organize the data in a meaningful, intelligible way.
To enable the reader to determine the nature and shape of the distribution
To facilitate computational procedures for measures of average and spread
To enable the researcher to draw charts and graphs for the presentation of data.
To enable the reader to make comparisons among different data sets.
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2.3 Histograms, Frequency Polygons, and Ogives
The histogram is a graph that displays the data by using contiguous vertical bars (unless the frequency of a class is 0) of various heights to represent the frequencies of the classes.
Step 1. Draw and label the x and y axes.
Step 2. Represent the frequency on the y axis and the class boundaries on the x-axis.
Step 3. Using the frequencies as the heights, draw vertical bars for each class.
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. The frequencies are represented by the heights of the points.
A Pareto chart is used to represent a frequency distribution for a categorical variable, and the frequencies are displayed by the heights of vertical bars, which are arranged in order from highest to lowest.