Definition of a Frequency Polygon
A frequency polygon is a graphical representation of a frequency distribution. It is constructed by plotting points that represent the midpoints of class intervals against their corresponding frequencies, then connecting these points with straight line segments. Essentially, it's a way to visualize the shape of a data set's distribution, often providing a smoother representation than a histogram for comparing multiple distributions.
Key Principles and Construction
To construct a frequency polygon, first create a frequency distribution with class intervals and their frequencies. Identify the midpoint (class mark) of each interval. Plot these midpoints on the horizontal (x) axis and the corresponding frequencies on the vertical (y) axis. To close the polygon and anchor it to the x-axis, add extra class intervals with zero frequency at both ends of the distribution, extending one class before the first and one after the last interval.
Practical Example of Use
Imagine a teacher wants to visualize the test scores of two different classes (Class A and Class B) on the same graph. Instead of overlapping two histograms, which can be messy, they could use two frequency polygons. By plotting the midpoints of score ranges (e.g., 50-59, 60-69) against the number of students achieving those scores for each class, they can easily compare the spread, central tendency, and shape of the score distributions side-by-side on a single chart.
Importance and Applications
Frequency polygons are important for quickly understanding the shape, spread, and central tendency of a data set. They are particularly useful when comparing two or more frequency distributions on the same graph, as the line segments make overlapping trends easier to discern than stacked bars. Applications span various fields, from analyzing student performance and economic data to tracking manufacturing defects or population age distributions.