Cumulative Frequency

To learn about Cumulative Frequency let us first understand what Frequency distribution is

. Frequency distribution is used to organize a given data. In this process the data is categorized and the number of observations is shown in each category using tally marks.

We can Define Cumulative Frequency as the sum of all the frequencies to the given value; it is also referred to as the running total of all the frequencies to a given value or to a certain level. Let us consider an example data, in a survey 15 people were asked about how many pets they had. The following is the Cumulative Frequency table for the given data.

Number of petsfrequencycumulative frequency

0 44

1 64+6=10

2 210+2=12

>2 312+3 = 15

In the above cumulative frequency table, we can see that in the cumulative frequency column each time the frequency of the previous row is added to get the next value, it is the running total of frequencies. To graph the given data, we take the number of pets on the x-axis and the cumulative frequency on the y-axis. Then we join the points to get a curve, this curve obtained is the cumulative frequency distribution graph of ungrouped data.

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The following are the marks of 10 students in a class test; 39, 89, 75,90,36,78,96,64,48,88.The given data is a grouped data and hence we need to divide data into classes with upper and lower boundaries. The least number is 39 and so, the lower bound is taken as 35 with an interval of 10. The data is tabulated in the cumulative frequency table with four columns, lower bound, upper bound, frequency and cumulative frequency. Then we plot the points on the graph, taking the upper bound on the x-axis and the cumulative frequency on the y-axis. The points are joined, the starting point being 35 on the x-axis(it being the lower bound); we get a polygon which is the cumulative frequency polygon of the given marks.

Cumulative Relative Frequency Distribution is the distribution got by the quotient of the cumulative frequency of a particular value and the sample size of the data.

Cumulative Relative Frequency= Cumulative frequency of a value/sample size of the data

The following are the temperatures recorded in a city in a week in a particular month. 31,30,27,29,30,27 28. Before tabulating the Cumulative Relative frequency Distribution, let us arrange the data in the ascending order, we get; 27,27,28,29,30,30,31

Temperaturefrequency cumulative frequencycumulative relative frequency

27 222/7=0.29

28 1 2+1=33/7=0.43

29 1 3+1=44/7=0.57

30 2 4+2=66/7=0.86

31 1 6+1=77/7=1

by:Omkar Nayak

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