This most commonly used central tendency is calculated by adding all the observations in the series and dividing it by the total number of observations. The formula for mean is:
It represents the extent to which each value contributes to the total.
Properties of Arithmetic Mean:
The sum of deviations of the observations from their arithmetic mean is always Zero:
Each value when subtracted from the mean then added gives us zero.
This means in a way the A.M. (Arithmetic Mean) balances each value.E.g. the A.M. of: 3, 5, 7, 9, 11 will be:
Only the arithmetic mean can be used for further mathematical treatment.
E.g. we can add the arithmetic means of two different sets of data to find their combined arithmetic mean.
Arithmetic mean is representative of each and every number in the series, therefore if even one number is missing or falls under open ended class interval, the arithmetic mean can’t be found.
This means that the start point and the end point should be specified.
E.g. we require to take out mean of 100 people having IQ>80 and IQ<135. 5 people don’t fall under this range therefore, we’ll take out the mean of the 95 which fall in that range and since there is no specific range for the rest of the 5, we ignore them.
Due to this disadvantage and because that arithmetic mean can’t be used when there is a huge variation in the data of the series, Median is used.