Arithmetic mean is the sum of the numerical values of each and every observation, divided by the total number of observations. For example- If we have 10 men working at salary of 12000$ each then the arithmetic mean will be as follows :_
A.M.= (12000 x 10 )/10 = 12000$.
- Another example - If Ram eats 10 apples , Shyam eats 12 apples and Sita eats 8 apples then their A.M. Will be = (10+12+8)/3= 30/3= 10 apples.
So , in general formula we can say that the Arithmetic Mean of a set of observations is equal to the sum of total numerical value of the observations divided by the no. of observations as we have seen above.
The arithmetic mean is denoted by the x̄ .
Geometric Mean :
Geometric Mean is defined as the nth root of product of n numbers . It is also a kind of mean or average like Arithmetic mean but here multiplication is used instead of addition likewise in A.P.
The reason for so is because geometric mean is used for those kind of set of numbers whose values are meant to be grow or multiply in nature like growth function. Example can be of population growth or financial investment interest growth rate.
For a set of numbers a1, a2, a3.....aN , the geometric mean is defined as the
Capital pi notation is the figure shown above and its nth root is taken to get the geometric mean of the set of given numbers.
Example-(1) The geometric mean of two numbers 2 and 4 is just the square root of the product of 2 and 4 i.e., 4.
(2) The geometric mean of three numbers 1,3,and 9 is the cube root of the product of 1,3and 9 (=27) i.e., 3.
Harmonic Mean
Harmonic Mean is the also one of the kinds of average like others discussed but it is used where average rate is desired.
By definition , it is the reciprocal of the arithmetic mean of the reciprocals of the given set of observations. Example:-
Difference between A.M. , G.M. and H.M.
Relationship between A.M. , G.M and H.M.
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