



Arithmetic Mean Of Individual Observations 
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Arithmetic Mean Of Individual Observations
If x_{1}, x_{2}, x_{3}, ..., x_{n} are n values of a variable X, then the arithmetic mean or simply the mean of these values is denoted by and is defined as
Here, the symbol denotes the sum x_{1}, x_{2}, x_{3}, ..., x_{n}.
Or we can say, the arithmetic mean of a set of observations is equal to their sum divided by the total number of observations.







Example: If the mean of 5, 3, 7, p and 10 is 8, find the value of p.
Solution: Since 8 is the mean of 6, 4, 7, p, 10.
Therefore, 8 = (5 + 3 + 7 + p + 10) / 5
=> 40 = 25 + p
=> p =15.
Example: Find the sum of the deviations of the variate values 3, 4, 8, 11, 14 from their mean.
Solution: Recall that the deviations of the values x_{1}, x_{2}, x_{3}, ..., x_{n} about A are
x_{1}  A, x_{2}  A, x_{3}  A, ..., x_{n}  A
Let
be the mean of the values 3, 4, 8, 11, 14.
Then, = (3 + 4 + 8 + 11 + 14) / 5 = 40/5 = 8
Now, sum of the deviations of the values 3, 4, 8, 11, 14 from their mean i.e. 8 is given by
(3  8) + (4  8) + (8  8) + (11  8) + (14  8) = 5 4 + 0 + 3 + 6 = 0






