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Unit-27: Measures of Central Tendency: Mean, Median, Mode

2. Median is amongst the elements given. therefore, it represents the entire population. its note
value is dependent upon all elements.
3. if we know the value of all elements then without knowing the result of all elements we can
find out the median. There is no need to find out the frequencies of the last element to find
out the median, we only need to know the value of elements.
4. Unlike arithmetic average there is no effect of very big or very small value on calculation
of median.
5. the value of median remains unaltered even after addition of some elements.
6. Median is most useful in those situations when the subject of study is such that it cannot be
measured in absolute terms such as knowledge of a child, etc.

Demerits of Median

in spite of above merits, median also has some demerits which are as follows-
a. Median cannot be calculated using algebraic methods i.e. we cannot find out the median
of two or more series cumulatively if we know their separate medians. in other words, we
cannot find out a common median that represents the other series accurately whose separate
medians are given. it is because of this reason that the median of a given series is the middle
element of that series and is nowhere related to the other series.
b. similar to mean, median also sometimes does not represent the real situation i.e. median
does not apply to any unit fully because median can be located in such a place in the series
where very less or no element is similar to it.
c. if there is too much difference or deviation in the series then sometimes median is not the
correct representative i.e. if there is too much difference in the details of the elements then
the results can be misguiding.

27.10 Mode

in any series, the value that appears the most is called as the mode. in this way mode is the value of
most commonly occurring value in the series. this is that value or result of the series that appears most
commonly in the series and it is that result around which the values of elements gather the most. the
easiest meaning of mode is that it is the value obtained by most of the people. for example, if in an
examination 10 students secure 7,9,7,5,8,12,7,6,8 then 7 will be called as mode because this number is
obtained the most or the number of students obtaining 7 marks is the most. From the given definitions,
the meaning of mode will be clearer.

Definition of Mode

Gilford has defined the mode like—“ Mode is that point in the distribution where there is highest
frequency.”
Dr.Chaturvedi writes “Mode is defined as that dimension of the variable that is most commonly
occurring or the point of highest frequency or the point of highest density. Mode is the value of that
element in the series that has the highest special or common characteristics.”
In our daily life we often hear that the average height of an Indian is 5’6”; the colour of Indians is
black; most of the people are honest; there are 300 words in a page, etc. In all these statements, the
word honest denotes mode. for example, when we say that the average height of an indian is 5’ 6’’
than it means that the value of indians with height 5’ 6’’ is highest in india.

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