A graph showing the cumulative frequency (or cumulative relative frequency) of a variable as a curve, with the x- axis showing the values of the variable and the y- axis showing the respective cumulative frequency is called Cumulative Frequency Curve (Ogive). It is also known as a cumulative distribution function (CDF)
Example:
The table below shows the cumulative frequency distribution of masses of cakes in Cocobakes made at a festival:
1. Quartiles
The three values which divide the whole data into four equal parts are called quartiles. Quartiles are usually denoted by Q1, Q2 and Q3. The lower quartile Q1 divides the data in 1 : 3. The middle quartile Q2 divides the data in 1 : 1. It is infect nothing different from median of data. The upper quartile Q3 divides the data in 3 : 1.
When data is arranged in some order, it can be represented by a single value that lies exactly at the centre of data. "The central or middle most value of an arranged data is called its median".
The quartiles can also be estimated graphically from a cumulative frequency polygon.
To estimate Q1 (lower quartile), mark on y- axis. Draw a line parallel to x- axis from that point to intersect cumulative frequency polygon. Drop a perpendicular from this point of intersection to x- axis. The value of data where the perpendicular meets x- axis is lower quartile Q1
Similarly, Q2 and Q3 can be estimated from cumulative frequency curve, by marking and on y- axis and following the same procedure used for Q1.
Example:
The scores on a test were compiled into a dataset with the following quartiles: Q1 = 40, Q2 or median = 70, Q3 = 90
What percentage of students scored above 90 on the test?
Solution: From the quartiles it is obvious that one fourth (25 percent) of the students scored above 90.