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Measures of Central Tendency: In the study of a population with respect to one in which we are
interested we may get a large number of observations. It is not possible to grasp any idea about the
characteristic when we look at all the observations. So it is better to get one number for one group. That
number must be a good representative one for all the observations to give a clear picture of that
characteristic. Such representative number can be a central value for all these observations. This central
value is called a measure of central tendency or an average or a measure of locations. There are five
averages. Among them mean, median and mode are called simple averages and the other two averages
geometric mean and harmonic mean are called special averages.
Characteristics for a good or an ideal average: The following properties should possess for an ideal
average.
1. It should be rigidly defined.
2. It should be easy to understand and compute.
3. It should be based on all items in the data.
4. Its definition shall be in the form of a mathematical formula.
5. It should be capable of further algebraic treatment.
6. It should have sampling stability.
7. It should be capable of being used in further statistical computations or processing.
Arithmetic mean or mean: Arithmetic mean or simply the mean of a variable is defined as the sum of
the observations divided by the number of observations. If the variable
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