Algebra1: Properties of Arithmetic Mean

 Properties of Arithmetic Mean 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 The sum of the deviations of a set of n values x1, x2, x3, ..., xn measured from 50 is -10 and the sum of deviations of the values from 46 is 70. Find the values of n and the mean.
Solution We have,

 - 50n = -10
and,
 - 46n = 70
Subtracting equation (ii) from equation (i), we get
- 4n = - 80 => n = 20
Putting n = 20 in equation (i), we get
 -50x20 = -10

 = 990

 Mean = 1/n = 990/20 = 49.5
Hence, n = 20 and mean = 49.5

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