Mode definition

Mode (statistics) is the value of the variable corresponding to the maximum of the ideal curve which gives the closest possible fit to the actual distribution of the frequency. It represents the value which is the most frequent or typical, the value which is, in fact, the fashion. The mode is sometimes denoted by writing the sign ? over the variants symbol, for example X? denotes the mode of the values X1,X2, …. Xn.

Mode formula:

It is evident that, mode is to be determined by inspection only. There is no stereotyped method listed for determination of the mode for a data set. It purely depends on the intuitions of the statistician or researcher. However there is an empirical relation between the mean, median and mode.
Mode = Mean – 3*(Mean – Median).
The above relation holds good with surprising closeness for moderately asymmetrical distributions.  Putting that in words, we say that the median lies one third of the distance mean to mode from the mean towards the mode.

Usually mode represents a single humped distribution unless specifically stated otherwise. When the distribution is of a complicated form, there may be more than one mode. Such distributions are therefore sometimes called multimodal. The mean and the median are still unique for such distributions.

What is mode for grouped frequency distribution:

Based on how we define mode, it is in fact difficult to determine the mode for grouped frequency distributions that are more common in practice. At max we can find the class with the maximum frequency. But beyond that it’s no use giving merely the mid value of the class interval into which the greatest frequency falls, for this is entirely dependent on the choice of the scale of the class intervals. It is again no use making the class interval very small to avoid error on that account, for the class frequencies will them become small and the distribution irregular. What we actually want to arrive is at the mid value of an interval for which the frequency would be a maximum, if the intervals could be made indefinitely small and at the same time the number of observations be so increased that the class frequencies should run smoothly. As the observations cannot, in a practical case, be indefinitely increased, it is evident that some process of smoothing out the irregularities that occur in the actual distribution must be adopted, in order to ascertain the approximate value of the mode.

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