WHAT IS MEDIAN ???
Median is the positional average of measures of central tendency. It is the middle value of the series. It is the value that divides the series into two equal parts. Thus, the values less than and more than median will be equal. It is denoted by M.
ACCORDING TO PROF. L R CONNOR
“The median is that value of the variable which divides the group into two equal parts, one comprising all values greater than and other, all values less than median.”
ACCORDING TO HORACE SACRIST
“Median of a series is the value of the item, actual or estimated, when a series is arranged in an order of magnitude which divides the distribution into two parts.”
To calculate the M, it is necessary to arrange the series. In case of odd series, the value lies in the series but in case of even series, the value is indeterminate and it does not similar to the values present in the series.
MERITS OF MEDIAN
EASY TO UNDERSTAND: This measure is just the middle value of the series after arranging the series in ascending or descending order. So it is easy to understand and explain the it.
EASY TO CALCULATE: There is no complex calculations involved. It is the middle value of the arranged series.
CALCULATION IN OPEN END OR UNEQUAL CLASS INTERVALS: There is no difficulty in calculation in the case of open end class intervals or unequal class intervals. The series needs no conversion.
NOT AFFECTED BY EXTREME VALUES: M is just the middle value of the series. It is that measure of central tendency which is least affected by the values of extreme items. So in case of inclusion of any extreme item in the series, there will be nominal effect on the value of median.
QUALITATIVE DATA: It has the advantage of being calculated in case of qualitative data like playing habits, beauty, honesty, intelligence etc.
BASE FOR OTHER MEASURES: It is actively used a s base for other statistical measures like Mean Deviation, Skewness and sampling etc.
CAN BE CALCULATED GRAPHICALLY: It can be located graphically. “Less than Ogive” and “More than Ogive” curves are used to locate the median graphically.
NOT BASED ON ALL OBSERVATIONS: It is not the true representative of the series as its value is not based upon all the observations of the series.
DIFFICULTY IN ARRANGING DATA: In case there is large number of observations available, then it is difficult to arrange the data in ascending or descending order.
UNRELIABLE MEASURE: As the calculation of M is not based on any concrete formula, it is an unreliable measure.
NOT CAPABLE OF FURTHER ALGEBRAIC TREATMENT: It is not capable of further algebraic treatment. If its value is known, it is not possible to find out the number of observations.
BASED ON ARITHMETIC MEAN: It is based on Mean if the number of values is even. The mean of two middle items is calculated then to find out the median.
COMBINED MEDIAN CANNOT BE CALCULATED: There is no technique to find out the combined median if the values of two or more series are given.