Adding all the observations and dividing the sum by the number of observations results the arithmetic mean. Suppose we have the following observations:
10, 15,30, 7, 42, 79 and 83
These are seven observations. Symbolically, the arithmetic mean, also called simply
x = åx/n, where x is simple mean.
= 10 + 15 + 30 + 7 + 42 + 79 + 83/ 7
= 266/7= 38
It may be noted that the Greek letter m is used to denote the mean of the population and n to denote the total number of observations in a population. Thus the population mean m = åx/n. The formula given above is the basic formula that forms the definition of arithmetic mean and is used in case of ungrouped data where weights are not involved.