Definition of cumulative frequency: According to Cumulative Frequency Definition A tabular display of data showing how many observations lie above or below certain values. The frequencies are grouped-frequencies or class-frequencies. If however the frequency of the first class is added to that of the second and this sum is added to that of the third and so on, then the frequencies so obtained are known as cumulative frequencies. There are two types of cumulative frequencies – less than and greater than. For less than cumulative frequencies we add up the frequencies from above and for greater than cumulative frequencies we add up frequencies from below. The value of the variable and the corresponding frequencies written together form a cumulative frequency distribution.
Cumulative relative frequency distribution: The display of a data set that shows the fraction or percentage of the total data set that falls into each of a set of mutually exclusive and collectively exhausted classes. Let us understand what is Relative Cumulative Frequency? We can define the relative cumulative frequency = cumulative frequency of a particular value /the total number of data or in other word , the quotient of cumulative frequency of any particular data and the total number of data.. The relative cumulative frequency can be expressed as a percentage.
Definition of Cumulative Frequency: Let us define Cumulative Frequency In a discrete frequency distribution the cumulative frequency of a particular value of the variable is the total of all the frequencies of the values of the variable which are less than or equal to the particular value.
Cumulative frequency polygon: The technique of drawing the cumulative frequency polygons and cumulative frequency curves or ogives is more or less the same. The only difference is that in case of simple frequency curves and polygons the frequencies are plotted against class marks of the class interval whereas in case of a cumulative-frequency polygon or curves the cumulative frequencies are plotted against the lower or upper limits of the class intervals depending upon the manner in which the series has been cumulated. There are two methods of constructing a frequency polygon and an ogive.
Let us discuss the two methods: (i) less than method (ii) more than method.
Less than method: To construct a cumulative-frequency polygon and an ogive by less than method, we use the following algorithm:
Step 1: Start with the upper limits of class intervals and add class frequencies to obtain the cumulative frequency distribution.
Step 2: Mark upper class limits along X-axis on a suitable scale.
Step 3: Mark cumulative frequencies along Y-axis on a suitable scale.
Step 4: Plot the points (xi, fi), where xi is the upper limit of a class and fi is the corresponding cumulative frequency.
Step 5: Join the points obtained in step 4 by a free hand smooth curve to get the ogive and to get the cumulative-frequency polygon join the points obtained in step 4 by line segments.
More than method: To construct a cumulative-frequency polygon and an ogive by more than method, we use the following steps:
Step 1: Start with the lower limits of class intervals and from the total frequency subtract the frequency of each class to obtain the cumulative frequency distribution.
Step 2: Mark lower class limits along X-axis on a suitable scale.
Step 3: Mark cumulative frequencies along Y-axis on a suitable scale.
Step 4: Plot the points (xi, fi), where xi is the lower limit of a class and fi is the corresponding cumulative frequency.
Step 5: Join the points obtained in step 4 by a free hand smooth curve to get the ogive and to get the cumulative frequency polygon join the points obtained in step 4 by line segments.
No comments:
Post a Comment