Ogives (Cumulative Frequency Curves)

An ogive (pronounced 'oh-jive') is a graph of a cumulative frequency distribution — it shows, at a glance, how many observations lie below (or above) any given value, rather than how many observations fall into any one class. There are two kinds, built from two different ways of accumulating frequency:

Reading the median from an ogive. Because the less-than ogive is built up of straight line segments joining known points, the value of the variable at which the cumulative frequency equals $N/2$ (half the total number of observations) can be located by finding which segment it falls on and reading (or computing, using that straight-line segment) the corresponding X-value — this X-value is the median of the distribution. The same value can also be located as the X-coordinate of the point where the less-than ogive and the more-than ogive intersect, since at that meeting point exactly half the observations lie on either side. Worked Example 7 and Exercise Question 6 both demonstrate this technique in full. …