Mean, median and mode are all different measures of central tendency or the average but they are all different from each other. A comparison of the three is therefore necessary. Letus suppose there are a set of five observations - 1, 1, 2, 5, and 6. The mean is what most people call the average and it is found by adding all these numbers and dividing it with the number of observations: I. + 1 + 2 + 5 + 6 = 15/5 = 3. The median on the other hand is one where half the values are below and half the values are above. In our above observation set, the median is 2 because there are 2 observations (5 and 6) greater than 2 and two (1and1) which are less than 2, making it the median. The mode is the observation that is repeated the maximum number of times. therefore in our observation set it is 1 because 1 is the only number that occurs twice, making it the mode. The choice of which method to use depends on the following considerations.
1. Rigidly defined - Mean and median are rigidly defined whereas mode is not. So as far as rigidity is concerned, mean and median are better than mode.
2. Based on all observations - An average should be based on all the observations of a series. This is met only mby mean and not by median and mode.
3. sampling stability - When the requirement is of least sampling variations, then mean is the best.
4. Further algebraic treatment - Mean only satisfies this characteristic, and because of this most of the stastical theories use mean as a measure of central tendency.
5. Easy to understand and calculate - An average should be easy to understand and easy to interpret. This characteristic is satisfied by all the three averages.
6. The measure of central tendency should not be undly affected by the extreme observations. The mode is the most suitable average from this point of view. Median is slightly affected whereas mean is very much affected by the presence of extreme observations.
