Histograms, polygons, ogives and line graphs

Frequency distributions are drawn in special ways:

• A histogram is a set of adjacent rectangles (with no gaps between them), drawn on the class boundaries. The area of each rectangle is proportional to the frequency of its class. If the classes have unequal widths, the heights must be adjusted to the frequency density (frequency ÷ class width). A histogram is drawn only for a continuous variable, and it can be used to find the mode.
• A frequency polygon is made by joining the mid-points of the tops of the histogram's rectangles with straight lines. To close it, extend it at each end to the base, at the mid-points of the empty classes just before the first class and after the last.
• A frequency curve is a smooth, freehand curve drawn through the points of the polygon.

Ogives (cumulative frequency curves) come in two kinds:

• A 'less than' ogive: the cumulative frequency (how many values are below each point) is plotted against the upper limits of the classes. It rises from left to right.
• A 'more than' ogive: the cumulative frequency of values above each point is plotted against the lower limits. It falls from left to right.

When both are drawn on the same graph, they cross at the median.

An arithmetic line graph (time series graph) shows how a value changes over time. Time goes on the X-axis, and the values on the Y-axis. It shows the trend (rising or falling) and any periodic ups and downs. Two lines on one graph, such as a country's imports and exports, can be compared year by year.