Measures of Central Tendency

Definition: Measures of Central Tendency helps in identifying the single value around which all the data in a group (observations) have a tendency to cluster. Simply, a measure of central tendency is the value considered as the most representative figure of the entire data set.

A measure of central tendency helps in identifying the center of all the observations and therefore is also called as Statistical Averages or Averages or Measures of Central Location. The central tendency helps in condensing the large data into a single value that represents the entire data set. Thus, central tendency is very useful when the data under study is very large.

A measure of central tendency also helps in comparing one data set with another. Such as if there are two samples of girls studying in two different schools and their marks in class 12^th are needed to be compared.  Then by calculating the average marks for each sample an easy comparison between the girls can be drawn.

Also, the central tendency helps in comparing one value of data with the entire data set. For example, if a boy obtained 50% marks in science can compare with the average marks obtained by each student to find out where he stands in class.

Basically, there are three important measures of central tendency:

1. Mean: The mean is the most common measure of central tendency. It is the value obtained by dividing the sum of all the observations by the number of observations in the dataset. Symbolically:
2. Median: The median is a positional average, basically used in the context of qualitative data, such as intelligence, etc. It divides the data into two equal parts where half of the items are less than the median while the half of the part is greater than the median. Therefore, the data set is first arranged in either the ascending order or the descending order. Such as, if the number of observations in the dataset:

   a) ‘n’ is odd:
   

   b) ‘n’ is even:

   

3. Mode: In a data set, the most frequently occurring item or observation is mode. For example, a manufacturer of cloth wants to know the size which most frequently ordered by the customers so that he can manufacture a large quantity of that size.

Thus, these are the measures of central tendency used to find out the most representative value of the dataset.