Sample Mean Formula

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Sample mean of a set of observations in their sum divided by the number of observations. Sample mean is simply the arithmetic average. The mean calculated for the sample data is denoted by x? (read as “x bar”). The number of values in a data set is denoted by n for a sample data and the sum of all values of x is denoted by ∑x, using the notations we can write the following formula for the sample mean.

 
Sample mean formula:-

Sample mean = Sum of all values of x / Number of values
x?= ∑x/ n

 
Example: - The following data give the numbers of hours spent partying by 10 randomly selected college students during the past week.

7          14        5          0          9          7          10        4          0          8

Compute the sample mean.
 

Solution: - Let us denoted the value in this example by x. Then the sum of the ten values of x is
∑x=7+14+5+0+9+7+10+4+0+8
    =64

Because the data set contains ten values, therefore n=10.

Substituting the values of ∑x and n in the sample mean formula, we obtain
            x?= ∑x/ n
              =64/10
              =6.4

Thus, the sample mean= 6.4
 

Other example: - Nixon Corporation manufactures computer terminals. The following data are the numbers of computer terminals produced at the company for 5 days.
24        32        27        23        35

Calculate the sample mean.
 
Solution: - Sample mean:
x?= ∑x/ n
  = (24+32+27+23+35)/5
  = 141 /5
  = 28.2

Therefore, the sample mean= 28.2


 

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