Some of the important characteristics of the arithmetic mean are:

 

  1. The sum of the deviations of the individual items from the arithmetic mean is always zero.  This means I: (x - x ) = 0, where x is the value of an item and x is the arithmetic mean. Since the sum of the deviations in the positive direction is equal to the sum of the deviations in the negative direction, the arithmetic mean is regarded as a measure of central tendency.
  2. The sum of the squared deviations of the individual items from the arithmetic mean is always minimum. In other words, the sum of the squared deviations taken from any value other than the arithmetic mean will be higher.
  3. As the arithmetic mean is based on all the items in a series, a change in the value of any item will lead to a change in the value of the arithmetic mean.
  4. In the case of highly skewed distribution, the arithmetic mean may get distorted on account of a few items with extreme values. In  such a case, it may cease to be the representative characteristic of the distribution.