Story of central tendency methods and their circumstances :(

In statistics, central tendency describes a central or representative value in a probability distribution.

There are 3 majorly known methods to calculate the central tendency.They are :

1.Mean

2.Median

3.Mode

These are the basics things everyone knew from school.They mean that,

Mean : It is the average of the given data points.

mean=sum of observations/no. of observations

Median : It is the middle value of the given data points.

Mode : It the most occured datapoint in the given set of datapoints.

so,when we read this,it seems so simple that thease can be known easily for a given set of datapoint.But,....there are some special circumstances occur when we use them.

Special circumstances of central tendancy methods :

Examples:

Mean : let's take a set of data points, 11,23,30,45,90,150. When we calculate the mean, the mean value is = (11+23+30+45+90+150)/6=349/6=58.16.

Here,the mean is separating the given set of data points as 2 groups ,where one contains the data points lesser than the mean,and the other contains the data points whose values are greater than the mean. then ,the groups are as given : 1) 11,23,30,45 and the 2)90,150,but actually,The numbers are not continuous,where they have a very great difference , where the greatest numbers 90 and 150 led to drastic increase in the mean value, otherwise ,the mean for the 1st 4 datapoints would be 27.25 which acts as a central tendency for those data points.

This is where, median comes into picture...But......This does have some special circumstances... :(

Median : When there is a case where there are 2 sets of 2 data points where they are 1)20,40 and 2)0,60 have the same mid values, then for a large dataset to perform statistics , how will we be able to find how distant they are ??

Mode : Let's take 2 sets of data points ,1 ) 1,1,2,3,4,5,5,9 2) 1,4,6,9,7,912,23

Here the 1st set of data points has 2 data points with highest and equal frequency i.e., with frequency 2, means, there are 2 modes, it is bimodal, sometimes, there exit multi-modal too...whereas, in the 2nd set of data points, there is no mode at all,.. so,which might lead to less straightforwardness of the data to interpret.

And ever, due to mode, we will only concentrate on the mostly occurred data, ignoring the remaning ones,and if the remaining were important, that might lead to loss of important insights.

So,everything that we think + ,has some - too, solving this euation of + and -,we should analyse the result of the equation and then move forward with the better method for performing statistics.