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Arithmetic Mean Of Individual Observations
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Arithmetic Mean Of Individual Observations
If x1, x2, x3, ..., xn 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 x1, x2, x3, ..., xn.
Or we can say, the arithmetic mean of a set of observations is equal to their sum divided by the total number of observations.
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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 x1, x2, x3, ..., xn about A are
x1 - A, x2 - A, x3 - A, ..., xn - 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
 
   
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