Overview: What Is A Frequency Distribution?
A frequency distribution can yield a lot of information about the results of an experiment or survey, even before any more complex statistical analysis is done. In its simplest form, a frequency distribution is just an organized tally of how many times an event occurs. It can be stated as a number or as a percentage. For example, suppose a biologist is studying types of aquatic plants that grow in a particular wetlands area. Knowing the numbers of different species, as well as the density of plants per square foot, will help make decisions about the types of nutrients that are available to support birds, fish, and other animals that are part of the ecosystem.
Should a Frequency Distribution Be Grouped or Ungrouped?
The highest value, the lowest value, and the most frequent occurrence (the mode) are usually the first parts of the pattern to appear. If the difference between the highest and lowest score is small, or if all the values are close together, then it might be easy to see the pattern in the data. That is not often what happens, however. Usually, the data are more spread out, and then it is more useful to group them into intervals that are all the same size. The next step is often to graph them by frequency or in a bar graph to visualize the relationships. A stem-and-leaf display is another way to plot raw data in a frequency distribution.
What Is the Shape of the Frequency Distribution?
Graphing the data from the frequency distribution will also allow the researcher to see the shape of the data. While there are some distributions that are symmetrical (for example, the normal curve), most are not. Most are skewed toward one end or another, and some curves will have one, two, or even three waves where some scores are more frequent than others. Researchers can then make decisions about what further statistical tests to use.
What Is the Scale of Measurement Used?
If the measurement is just categorical, it is the nominal scale of measurement. One of the first questions in any survey is, “Are you male or female?’ If the measure involves ranking, it is ordinal. For example, in the alternative fuel survey, people were asked if they drove small, medium, or large cars. Other measurements at the interval or ratio scales involve values that are beyond counting or numerical ranking, such as temperature, time, length, or weight.
Statistical Tests on Frequency Alone
One of the most common statistical tests used when the measurement is categorical or ordinal is the chi square test. It tests whether or not there is a relationship between the independent variable and the dependent variable, and is easily calculated by hand (or in seconds with a computer). It is often used with data from surveys, as most of the responses are either counted or ranked.
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