Ways to Organize Data
When data is collected from a survey or an experiment, they must be organized into a manageable form. Data that is not organized is referred to as raw data. A few different ways to organize data include tables, graphs, and numerical summaries.
One common way to organize qualitative, or categorical, data is in a frequency distribution. A frequency distribution lists the number of occurrences for each category of data.
Step-by-Step Guide to Plotting Qualitative Frequency Distributions
The first step towards plotting a qualitative frequency distribution is to create a table of the given or collected data. For example, let's say you want to determine the distribution of colors in a bag of Skittles. You open up a bag, and you find that there are 15 red, 7 orange, 7 yellow, 13 green, and 8 purple. Create a two column chart, with the titles of Color and Frequency, and fill in the corresponding data.
To construct a frequency distribution in the form of a bar graph, you must first draw two axes. The y-axis (vertical axis) should be labeled with the frequencies and the x-axis (horizontal axis) should be labeled with each category (in this case, Skittle color). The graph is completed by drawing rectangles of equal width for each color, each as tall as their frequency .
Bar Graph
This graph shows the frequency distribution of a bag of Skittles.
Sometimes a relative frequency distribution is desired. If this is the case, simply add a third column in the table called Relative Frequency. This is found by dividing the frequency of each color by the total number of Skittles (50, in this case). This number can be written as a decimal, a percentage, or as a fraction. If we decided to use decimals, the relative frequencies for the red, orange, yellow, green, and purple Skittles are respectively 0.3, 0.14, 0.14, 0.26, and 0.16. The decimals should add up to 1 (or very close to it due to rounding). Bar graphs for relative frequency distributions are very similar to bar graphs for regular frequency distributions, except this time, the y-axis will be labeled with the relative frequency rather than just simply the frequency. A special type of bar graph where the bars are drawn in decreasing order of relative frequency is called a Pareto chart .
Pareto Chart
This graph shows the relative frequency distribution of a bag of Skittles.
The distribution can also be displayed in a pie chart, where the percentages of the colors are broken down into slices of the pie. This may be done by hand, or by using a computer program such as Microsoft Excel . If done by hand, you must find out how many degrees each piece of the pie corresponds to. Since a circle has 360 degrees, this is found out by multiplying the relative frequencies by 360. The respective degrees for red, orange, yellow, green, and purple in this case are 108, 50.4, 50.4, 93.6, and 57.6. Then, use a protractor to properly draw in each slice of the pie.
Pie Chart
This pie chart shows the frequency distribution of a bag of Skittles.