statistics Statistics (from German language, German: ', "description of a State (polity), state, a country") is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data. In applying statistics to a s ...

, 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 In probability theory and statistics, the cumulative distribution function (CDF) of a real-valued random variable X, or just distribution function of X, evaluated at x, is the probability that X will take a value less than or equal to x. Ever ...

* 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 probability theory and statistics, the empirical probability, relative frequency, or experimental probability of an event is the ratio of the number of outcomes in which a specified event occurs to the total number of trials, i.e. by means no ...

. The ogive for the

normal distribution In probability theory and 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 ...

(on one side of the mean) 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 "Foliate ...

ogival An ogive ( ) is the roundly tapered end of a two- or three-dimensional object. Ogive curves and surfaces are used in engineering, architecture, woodworking, and ballistics. Etymology The French Orientalist Georges Séraphin Colin gives as ...

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

* {{statistics-stub Functions related to probability distributions

Creation

Finding percentages

See also

References

Bibliography