Measures of Central Tendency or ‘averages’ reduce the huge mass of data into single figures. These single figures represent the entire distribution. There are certain requirements of a good average. Arithmetic mean, median and mode are the most commonly used averages. Each has got its advantages and disadvantages. Arithmetic mean satisfies almost all the characteristics of a good average. Therefore, it is the best average. But in particular cases median and mode are suitable.
Sum of the values of items/ Number of items
Arithmetic mean is defined as the sum of the values of a group of items divided by
the number of items, or A.M.=
Weighted Arithmetic mean is better than simple arithmetic mean in certain cases where different importance should be given to different items in the series as in the case of computation of Index Numbers.
Median is a positional average. It is the value of the middle item of a series when it is arranged either in ascending or in descending order of magnitude. It is the value of N/2th item in case of continuous series or (N+1)/2th item in case of discrete series where N stands for the number of items. Interpolation formula is adopted in the case of continuous series. Median divides the series into two equal parts, one part having values greater than the median and the other less than it. Likewise Quartiles, Octiles, Deciles etc. divide the series into 4, 8, and 10 equal parts respectively. These are called as partition values.
Mode is also a positional average. It is the value of the item which has got the greatest frequency density in its immediate neighborhood. Interpolation formula is adopted to find out mode in case of continuous series. Mode is affected by the frequencies of preceding and succeeding groups: In case of bi-modal and multi-modal series, grouping and analysis table are necessary.