Graphic Presentation — Frequency Polygon and Frequency Curve

A frequency polygon is obtained by plotting each class's mid-value on the x-axis against its frequency on the y-axis, and joining the plotted points with straight lines. To close the figure into a proper polygon, one extra class (with frequency 0) is imagined at each end of the distribution, and the polygon is joined down to the x-axis at those two points.

A frequency polygon can be drawn in either of two ways: directly from the mid-values and frequencies of a distribution, or by first drawing the histogram and then joining the mid-points of the tops of adjoining rectangles — both methods give the same polygon, and the area enclosed by the polygon equals the area enclosed by the histogram (this equality is the reason the polygon must be closed down to the x-axis at a zero-frequency point on each side, not just left open).

A frequency curve is a smoothed, free-hand curve drawn through the same (mid-value, frequency) points as the polygon, instead of straight line segments. It is used when the underlying variable is genuinely continuous and a smooth trend (rather than the polygon's angular shape) is wanted — for example, to show the general shape of a distribution as symmetric, or skewed to one side (a comparison taken up in more depth in the Skewness chapter later in this Gujarat Std-11 statistics syllabus). …