Frequency Distribution

Frequency distributions are like frequency polygons; however, instead of straight lines, a frequency distribution uses a smooth curve to connect the points and, similar to a graph, is plotted on two axes: The horizontal axis from left to right (or x axis) indicates the different possible values of some variable (a phenomenon where observations vary from trial to trial). The vertical axis from bottom to top (or y axis) measures frequency or how many times a particular value occurs.

For example, in Figure 1 , the x axis might indicate annual income (the values would be in thousands of dollars); the y axis might indicate frequency (millions of people or percentage of working population). Notice that in Figure 1 the highest percentage of the working population would thus have an annual income in the middle of the dollar values. The lowest percentages would be at the extremes of the values: nearly 0 and extremely high.

Figure 1 A symmetric bell curve.

The negatively skewed curve, shown in Figure 2 , is skewed to the left. Its greatest frequency occurs at a value near the right of the graph.

Figure 2 Negatively skewed bell curve.

The positively skewed curve (see Figure 3 ) is skewed to the right. Its greatest frequency occurs at a value near the left of the graph. This distribution is probably a more accurate representation of the annual income of working Americans than is Figure 1 .

Figure 3 Positively skewed bell curve.

Figure 4 shows a J-shaped curve.

Figure 4 J-shaped curve.

Unlike Figure 1 , a bimodal curve (shown in Figure 5 ) has two high points.

Figure 5 A bimodal curve has two maximum peaks.

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