Cumulative Frequency Cumulative Frequency In this unit we will learn about "Cumulative Frequency". Before we learn about the cumulative frequency and its existence, we must know the elementary terms related to cumulative frequency. When a large number of data is collected in wide range, then they are classified in several groups, based on the size of the value. These groups are formed of certain fixed size. Each of these groups which are of fixed size is usually called as intervals. A class interval always has a lower and the upper limit. These limits are the smallest and the largest extreme values of the particular range of the data. The number of times a particular data appears, in the data collection, is called the frequency of that range. The word "Cumulative Frequency" is derived from the word cumulate, which means successively adding of the frequencies of the successive class intervals given one after another. Thus we can say that the cumulative frequency of the given class interval is the figure which will represent the sum of all the previous class frequencies including the frequency of the class which contains the cumulative frequency.
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It means it contains the sum total of all the frequencies of all the sum data including the frequency of the class interval which contains it. The cumulative frequencies can be of less than type or more than type. If we talk about the cumulative frequency of the less than type, it will represent the total frequencies of all the classes which are less than and equal to the class value to which it refers and to which it relates. On other hand if we talk about the cumulative frequency of the more than one type, it will represent the total frequencies of all the classes which are more than and equal to the class value to which it refers and to which it relates. In other words we can say that the cumulative frequency is the frequency distribution showing the cumulative frequencies placed against the values of the variables, which are systematically arranged either in ascending or descending order. If we are given a table representing the range of the salary drawn by the number of people, then here the number of people which exist within the range of the salary is called the frequency of that particular data. Now in the next column if we calculate the cumulative frequency, then the data represented by the column of cumulative frequency will help us to find the number of people getting the salary less than or equal to that particular range. Sometimes we come across the open end data, which means that the data begins with the range “less than” at first data reading and it appears like “more than “. This type of data representation in the table is called “open end classes”. Moreover, the frequency of individual class interval can always be obtained by deducting the total of previous class interval from the cumulative frequency of the last class interval for which we need to find the frequency of the given class.
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We may note that the cumulative frequency of the first class interval is the frequency itself. Again when we find the class intervals are unequal, such a process will surely help to reduce the error that occurs in the tabulation and the classification of the data. Steps for constructing a less than Ogive chart (less than Cumulative frequency graph): 1. Draw and label the horizontal and vertical axes. 2. Take the cumulative frequencies along the y axis (vertical axis) and the upper class limits on the x axis (horizontal axis) 3. Plot the cumulative frequencies against each upper class limit. 4. Join the points with a smooth curve. Steps for constructing a greater than or more than Ogive chart (more than Cumulative frequency graph): 1. Draw and label the horizontal and vertical axes. 2. Take the cumulative frequencies along the y axis (vertical axis) and the lower class limits on the x axis (horizontal axis) 3. Plot the cumulative frequencies against each lower class limit. 4. Join the points with a smooth curve.
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