Graphs

Most people find visual representations to be useful in highlighting information obtained from sample observations. The information presented in a frequency distribution table can be more easily grasped if it is presented in a graphical format. Absolute, relative or cumulative frequencies can be represented in the graphs, depending on the particular objectives for creating the graph. There are various graphical means to visualize a frequency distribution; bar charts, histograms, pie charts and frequency polygons/ogives are among the most popular.

A bar chart graphs the frequency distribution of the data on an x-y coordinate system. The class intervals are plotted on the x-axis, the absolute (or relative) frequencies on the y-axis. Each interval is represented by a rectangle whose base corresponds to a class interval and whose height is equal to the frequency associated with the class interval.Â

A histogram is similar to a bar chart, but the base of the rectangle has a length exactly equal to the class width of the corresponding interval. As the rectangle is centered on the average of the lower and upper class limits, the rectangles of a class interval are adjacent to the rectangles of adjoining class intervals--there are no spaces between rectangles.

A frequency polygon plots (x,y) pairs on the x-y coordinate system, where x is the average of the lower and upper class limits of the interval and y is the absolute (or relative) frequency associated with the class interval. These (x,y) points are connected by straight lines; the polygon is then formed by plotting points corresponding to two additional class intervals, with frequency 0, at each end of the frequency distribution. As these two additional points will be plotted on the x-axis, they will form a polygon with the contiguous set of line segments joining the (x,y) pairs.

A frequency ogive is a frequency polygon that uses the cumulative frequencies of the frequency distribution (as opposed to absolute or relative frequencies) as the values plotted on the y-axis. Since the cumulative frequency is a non-decreasing function, i.e., the value of the cumulative frequency increases (or remains the same) as the upper class limit of the interval increases, the graph of the frequency ogive will also be non-decreasing as the value of the x-coordinate increases.

A pie chart displays the absolute (or relative) frequencies of the class intervals as sectors of a circle. Each sector in a pie chart corresponds to a class interval; the ratio of the area of the sector to the area of the circle (i.e., the ratio of the measure of the sector's central angle to 360) is equal to the relative frequency of the class interval.