Mean

The mean is one of the measures of central tendency. Mean implies the average of a dataset consisting of values. Mean makes sure that there is an equal distribution of values in a given dataset. Also, mean carries the symbol: ‘x?’.

Where, the bar above the letter x, represents the mean of x number of values. 

 

Following is the formula for mean:

x = (Sum of values ÷ Number of values)
 

Hence, 

x = (x1 + x2 + x3 +….+xn)/n
 

The above equation implies that the sum of all the values is divided by the number of values in that dataset.
 

While the above mean is called the arithmetic mean, a geometric mean, which indicates the central tendency of a set of numbers by using the product of their values, can also be calculated.

Following is the formula for the geometric mean:

Another type of mean is the harmonic mean which is generally used when the average of rates is desired. 

The harmonic mean is calculated by the formula given below:

Let us see an example for each of the mean types discussed above.

 

Consider these three values as 50, 51, 60.

 

The arithmetic mean (AM) of the above values will be:

50+51+60=  53.67

 

The geometric mean (GM) of the same values will be:

 

 

Lastly, the harmonic mean (HM) will be:

 

From the above example, one of the differences between the three means of the mean can be observed which is AM>(greater)GM>(greater)HM. Hence, AM is greater than GM and GM is greater than HM.