In statistics, an ogive, also known as a cumulative frequency polygon, can refer to one of two things: * any hand drawn graphic of a cumulative distribution function * any empirical cumulative distribution function. The points plotted as part of an ogive are the upper class limit and the corresponding cumulative absolute frequency or cumulative

relative frequency In statistics, the frequency (or absolute frequency) of an event i is the number n_i of times the observation has occurred/recorded in an experiment or study. These frequencies are often depicted graphically or in tabular form. Types The cumula ...

. The ogive for the

normal distribution In statistics, a normal distribution or Gaussian distribution is a type of continuous probability distribution for a real-valued random variable. The general form of its probability density function is : f(x) = \frac e^ The parameter \mu ...

resembles one side of an

Arabesque The arabesque is a form of artistic decoration consisting of "surface decorations based on rhythmic linear patterns of scrolling and interlacing foliage, tendrils" or plain lines, often combined with other elements. Another definition is "Foli ...

ogival An ogive ( ) is the roundly tapered end of a two-dimensional or three-dimensional object. Ogive curves and surfaces are used in engineering, architecture and woodworking. Etymology The earliest use of the word ''ogive'' is found in the 13th c ...

arch, which is likely the origin of its name.

Creation

Along the horizontal axis, the limits of the class intervals for an ogive are marked. Based on the limit values, points above each are placed with heights equal to either the absolute or relative cumulative frequency. The shape of an ogive is obtained by connecting each of the points to its neighbours with line segments. Sometimes an axis for both the absolute frequency and relative is drawn.

Finding percentages

Ogives, similarly to other representations of cumulative distribution functions, are useful for estimating centiles in a distribution. For example, we can know the central point so that 50% of the observations would be below this point and 50% above. To do this, we draw a line from the point of 50% on the axis of percentage until it intersects with the curve. Then we vertically project the intersection onto the horizontal axis. The last intersection gives us the desired value. The frequency polygon and ogive are used to compare two statistical sets whose number could be different.

References

Bibliography

* Dodge, Yadolah (2008). The concise Encyclopedia of Statistics. Springer. p. 395. {{statistics-stub Functions related to probability distributions