 # Mode Of Data & Statistics

Statistics deals with the presentation, collection and analysis of data and information for a particular purpose. To represent this data we use tables, graphs, pie-charts, bar graphs, pictorial representation and so on. After proper organization of the data it must be further analyzed to infer some useful information from it. For this purpose, frequently in statistics we tend to represent a set of data by a representative value which would roughly define the entire collection of data. This representative value is known as the measure of central tendency. By the name itself it suggests that it is a value around which the data is centered. These measures of central tendency allow us to create a statistical summary of the vast organized data. One such method of measure of central tendency is mode of data. Let us discuss about mode and its applications.

## Mode of Data

The value occurring most frequently in a set of observations is its mode. In other words, mode of data is the observation having the highest frequency in a set of data. There is a possibility that there exists more than one observation having the same frequency i.e. a data set could have more than one mode. In such a case the set of data is said to be multimodal.

Let us look into an example to get a better insight.

Example: The following table represents the number of wickets taken by a bowler in 10 matches. Find the mode of the given set of data. It can be seen that 2 wickets were taken by the bowler frequently in different matches. Hence, the mode of the given data is 2.

In case of grouped frequency distribution, calculation of mode just by looking into the frequency is not possible. To determine mode of data in such cases we calculate the modal class. Mode lies inside the modal class. The mode of data is given as: Where,

l = lower limit of the modal class

h = size of the class interval

f1 = frequency of the modal class

f0 = frequency of the class preceding the modal class

f2 = frequency of the class succeeding the modal class

Let us take an example to understand this clearly;

Example: In a class of 30 students marks obtained by students in mathematics out of 50 is tabulated as below. Calculate the mode of data given. The maximum class frequency is 12 and the class interval corresponding to this frequency is 20 – 30. Thus, modal class is 20 – 30.

Lower limit of the modal class (l) = 20, size of the class interval (h) = 10,

Frequency of the modal class (f1) = 12,

Frequency of the class preceding the modal class (f0) = 5,

Frequency of the class succeeding the modal class (f2)= 8

Substituting these values in the formula we get; 