Cumulative Frequency Distribution

The total frequency of all classes less than the upper class boundary of a given class is called the cumulative frequency distribution .Relative frequency is the fraction of total number of elements .There are two types of Cumulative  frequency distributions, as follows

1.    Less than cumulative frequency distribution

2.    More than cumulative frequency distribution

Please express your views of this topic Normal Cumulative Distribution by commenting on blog.

Cumulative distribution function in cumulative frequency distribution

In common terms, the cumulative frequency distribution is the sum of all the frequencies. A cumulative frequency distribution is a sum of a set of data showing the frequency or number of items less than or equal to the upper class limit of each class. The Cumulative distribution function (CDF), describe the Probability distribution of random Variable X

The random variable X is given by

X -> Fx(x) =P(X<=x),

P(X<=x) =The probability that the random variable x takes on a value less than or Equal to x.

FX(b) − FX(a) if a < b.

Where

F for cumulative distribution function

The probability density function f can write as follows:

F(x) = $\int_{-\infty}^x f(t)\,dt$

Where

f(t) means probability density function

Applications and uses of cumulative frequency distribution

Cumulative frequency gives the total number of outcomes that occurred up to some value. Cumulative frequencies are used in risk or reliability analysis. In frequency distribution, every bin has the number of values that lies within the range of values that define the bin. In a cumulative distribution, every bin has the number of data that falls within or below the bin. A graph contains a frequency distribution on the left, and a cumulative distribution of the same data on the right is called a cumulative frequency distribution

The main advantage of cumulative frequency distribution is that one doesn’t need to decide on a bin width or the frequency distribution analysis dialog, can choose among  number of ways to graph the resulting data.


I am planning to write more post on Limits at Infinity Rules and free online math tutor. Keep checking my blog.