In this article we will discuss about Mode:- 1. Meaning of Mode 2. Method of Determining Mode 3. Merits 4. Demerits.
Meaning of Mode:
Mode is another unit of measurement of central tendency which is used to obtain a quick estimate of central tendency. Mode is defined as the particular value which appears again and again for maximum number of times in a set of observations. In other words, mode is that variety or item in the series which shows highest frequency.
It is denoted by Mo or Z. Sometimes, in a series of data all the variants have equal frequency. In such a series there is no mode. In some series more than one data have equal frequency. In such series there may be more than one mode. Such a series is said to be multimodal series. That series is analysed properly to get the genuine mode.
Method of Determining Mode:
For different types of data, the methods of computation of Mode are different.
1. For non-grouped data:
If the values of all the items are given separately then the mode is the value of that item which shows largest frequency.
Example:
Find out the mode size of shoe from the following numbers of shoes 2, 7,4, 1, 7,7, 6, 7, 7, 6, 5, 3, 2, 2, 7, 7, 5 Mode = 7.
2. For discrete series of data:
Mode of discrete series of data is determined easily because the figure with highest frequency is mode of the series.
Example:
Determine the mode from the following data regarding the number of flowers per plant:
Solution:
The above Table of data distribution indicates that 5 flowers per plant is represented 35 times out of 129 plants which is the largest frequency. Therefore, the value of Mode is 5 flowers per plant.
For grouped data, the mode can be calculated by identifying the class with highest frequency by grouping method which is detailed as under:
1. Grouping Method:
When in a given series two or more classes show same frequency, mode cannot be determined by inspection method. Sometimes the frequencies of neighbouring classes effect the mode determination in such a way that a class other than the true mode class with highest frequency is treated as mode. In order to avoid such mistakes, grouping method is used to determine mode which is the best method.
Grouping method is outlined below:
Grouping Table:
For this, table is made in which first column is meant for observed items or classes and the next 6 columns are meant for frequency. In the first frequency column, the frequency of each item or class is mentioned. In the second frequency column, the given frequencies are grouped in pairs starting from first and the combined values of paired frequencies are mentioned.
In the third frequency column, the groups of two frequencies each are made starting from the frequency of the second item or class and the combined values are noted against different groups.
In the fourth frequency column groups of three frequencies each are made starting from the first frequency and the combined values of three frequencies in different groups are recorded.
In the fifth frequency column, the frequencies of first column are made into groups of three each starting from the second frequency and combined values of 3 frequencies of different groups are recorded.
In the sixth frequency column, the frequencies of first column are bracketed into groups of three each starting from the third frequency and the combined value of three frequencies is noted against each group.
2. Analysis Table:
This is made to record the items or classes represented by highest frequency of different columns.
3. Determination of Mode:
The value of item or class which is represented by highest in the analysis table is mode.
The grouping method for determining mode is illustrated by taking the example of the following data:
Example:
Find out the mode of the following series:
From the above analysis table it is clear that 34 fruits/plant appeared four times which has the highest frequency. Therefore, the mode (MO) = 34.
(iii) For classified Data:
First of all the class with highest frequency, i.e. Mode class is identified either by inspection method or grouping method and then the mode is calculated with the help of the following formula:
Let us take the following classified data table for calculation of mode here.
From the above data table it is apparent that the class 70-80 has highest frequency, i.t. 15. Therefore, 70-80 is the mode class.
The mode can now be calculated with the help of the following formula.
Example:
Calculate the mode of data presented in the following Table for 220 plants of a local variety of wheat.
The analysis table reveals that class 80-90 has the highest frequency. Therefore it is mode class.
Now the mode can be calculated with the help of the following formula.
Merits of Mode:
1. It is based on all values and can be subjected to further algebraic treatment.
2. It represents group as well as extreme items and is not affected unless they are in modal class.
Demerits of Mode:
1. It requires intricate calculation.
2. It cannot be used for further calculations and interpretations.