Page 205 - DSOC404_METHODOLOGY_OF_SOCIAL_RESEARCH_ENGLISH

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

c. it is necessary to know the values of all the elements separately for calculating arithmetic note
average. if some of the elements are left out then mean cannot be calculated whereas median
and mode can be determined.
d. Arithmetic average does not point out to progressive and regressive series and sometimes
misguiding results are also obtained from this. for example, if a student obtains 381, 427
and 502 marks in three-monthly, six-monthly and yearly exams respectively and another
student obtains 502, 427 and 381 marks respectively then the arithmetic average of the two
will be same and it cannot be determined that the two were increasing. similarly regressive
series can also not be shown by this.

27.8 Median

Median is that point which divides a given series into two equal parts. in this way 50 percent elements
are above the median and 50 percent elements are below the median. But for doing this it is essential
that we must arrange the values of variable quantities in a series either in ascending or descending
order first. In this reference it is noteworthy that median is never any special element but the result
of middle element.
Meaning and Characteristics of Median
According to Dr. Chaturvedi, “if a given series is arranged in ascending or descending order then the
median is the value of the middle element of the series.”
According to Ghosh and Choudhary, “Median is the value of that element in the series that divides
the series into two equal parts in which the first part of the series contains elements smaller than the
median and the second part contains elements greater than the median.”
From the above definitions’ it is clear that median is the value of the middle element of the series. For
example, if in a given class 31 students are arranged according to their heights the 16th student will
be the middle one and the value of his height will be the median of the height of 31 students because
height is a variable quantity. remember that 16 student is the middle student of the series but 16
th
is not the median of the series but the value of the 16 student will be the median. this way middle
th
element is not itself the median but it is the scale of measurement for median.
there are following characteristics of median based on the above description-
a. Median is not the middle element but the value of the middle element.
b. Median divides the series into two equal parts in which the first part of the series contains
elements smaller than the median and the second part contains elements greater than the
median.
c. it is essential to arrange the values of variable quantities in a series either in ascending or
descending order for calculating median.

27.9 Method of Calculating Median

the normal way to calculate median is that the series must be arranged in ascending or descending
order for example—1, 2, 3, 4, 5 or 5, 4, 3, 2, 1, thereafter find the middle element of the series, the value
of this middle element is the median. And if there are even numbers in a series, since there is no middle
element then the value obtained by dividing the sum of middle elements by two is the median.

Median of Simple Series

the given below two formulae’s are used for calculating the median in a simple series.

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