Mode
Mode (Z ) is that value which has the maximum concentration of observations around it. This can also be described as the most common value among the given observations. In discrete frequency distribution, the observation having the highest frequency is called Mode.
 If in an ungrouped data, any observation is not repeating, then Mode (Z) can be found using the relation
 In continuous frequency distribution, following formula is applicable:
Marks  0â€“20  20â€“40  40â€“60  60â€“80  80â€“100 
Students  5  18  48  12 
5

Marks  No. of Students 
0â€“20  5 
20â€“40  18 (f_{â€“1}) 
40â€“60  48 (f_{0}) 
60â€“80  12 (f_{1}) 
80â€“100  5 
Note: A distribution having one mode is called unimodal.
A distribution having two modes is called bimodal.
A distribution having more than two modes is called multimodal.
Properties of Mode
Merits
 It can be easily understood.
 It can be located in some cases by inspection.
 It is capable of being ascertained graphically.
 It is not affected by extreme values.
 It represents the most frequent value and hence it is very often in practice.
 The arrangement of data is not necessary if the items are a few.
Demerits
 There are different formulae for its calculations which ordinarily give different answers.
 Mode is determinate. Some series have two or more than two modes.
 It cannot be subjected to algebraic treatments. For example, the combined mode cannot be calculated for the modes of two series.
 It is an unstable measure as it is affected more by sampling fluctuations.
 Mode for the series with unequal classintervals cannot be calculated.
Comparison Among Mean, Median and Mode

Mean 
Median 
Mode 
Average 
It is a calculated average. 
It is a positional average. 
It is a positional average. 
Calculations 
It is based on all the observations. 
It is the middle most value which divides the series into two equal parts. 
It is the value around which the terms of the series tend to concentrate densely. 
Treatment 
It is capable of mathematical treatments. 
It is not capable of mathematical treatments. 
It is not capable of mathematical treatments. 
Items 
It involves all the items for calculations. 
Does not consider all the items. 
Does not consider all the items. 
Array 
Does not require arraying. 
Arraying of the values of the items in the series is essential. 
Arraying of the values of the items in the series is essential. 
Extreme Values 
It is affected by the extreme and abnormal values of the items in the series. 
It is not affected by the extreme values. 
It is not affected by the extreme values. 
Result 
There is only one mean. 
There is only one median. 
In a series, there may be one Mode or more than one Mode or no Mode. 
Reliability 
Most reliable measure 
Less reliable 
Less reliable 
Use 
It is simple and widely used in statistical treatment and interpretation. 
Not popular and is used only in appropriate cases. 
Not popular and is used only in appropriate cases. 