Merits and Demerits of Measures of Central Tendency
Answers
Explanation:
Measures of Central Tendency - Median
A median is a positional number that determines the position of the middle set of data. It divides the set of data into two parts. In which, one part includes all the greater values or which is equal to a median value and the other set includes all lesser values or equal to the median. In simple words, the median is the middle value when a data set is organised according to the magnitude. The value of the median remains unchanged if the size of the largest value increases because it is defined by the position of various value.
To evaluate the median the value must be arranged in the sequence of numbers, and the numbers should be arranged in the value order starting from lowest to highest. For instance, while evaluating the medium if there is any sort of odd amount of number in the list, the median will be the middle number, with a similar number presented below or above. However, if the amount is an even number than the middle pair must be evaluated, combined together, and divided by two to find the median value.
Meaning, Merits and Demerits of Median
Q.1 MEDIAN
“The median is that value of the variable which divides the group into two equal parts, one part comprising all values greater and the other values less than the median.”….L.R. Connor
Median is the middle value of the series when items are arranged either in ascending or descending order.
It divides the series into two equal parts. One part comprises all values greater than the median and the other part comprises all values smaller than the median.
Q.2-BRIEFLY EXPLAIN THE MERITS AND DEMERITS OF MEDIAN.
ANSWER:
(A) FOLLOWING ARE SOME OF THE MERITS OF MEDIAN:
(1) EASY TO CALCULATE AND SIMPLE TO UNDERSTAND
It is easy to calculate and simple to understand.
In many situations median can be located simply by inspection.
(2) NOT AFFECTED BY EXTREME VALUES
It is not affected by the extreme values i.e. the largest and smallest values. Because it is a positional average and not dependent on magnitude.
(3) RIGIDLY DEFINED
It has a definite and certain value because it is rigidly defined.
(4) BEST AVERAGE IN CASE OF QUALITATIVE DATA
Median is the best measure of central tendency when we deal with qualitative data, where ranking is preferred instead of measurement or counting.
(5) USEFUL IN CASE OF OPEN ENDED DISTRIBUTION
It can be calculated even if the value of the extremes is not known. But the number of items should be known.
(6) REPRESENTED GRAPHICALLY
Its value can be determined or represented graphically with the help of Ogive curves. Whereas it is not possible in case of Arithmetic Mean.
(B) FOLLOWING ARE SOME OF THE DEMERITS OF MEDIAN:
(1) ARRANGEMENT OF DATA IS NECESSARY
Since the median is an average of position, therefore arranging the data in ascending or descending order of magnitude is time-consuming in the case of a large number of observations.
(2) NOT BASED ON ALL THE OBSERVATIONS
It is a positional average and doesn’t consider the magnitude of the items.
It neglects the extreme values.
(3) NOT A REPRESENTATIVE OF
THE UNIVERSE
It is not dependent on all the observations so, it cannot be considered as their good representative.
In case there is a big variation between the data, it will not be able to represent the data.
(4) AFFECTED BY FLUCTUATIONS IN SAMPLING
It is affected by the fluctuations of sampling and this effect is more than in case of Arithmetic Mean.
(5) LACK OF FURTHER ALGEBRAIC TREATMENT
It is a positional average so further algebraic treatment is not possible. Like, we cannot compute the combined median of two groups of data.
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It is the only measure of central tendency which is useful for nominal data. There may be more than one modal value (known as bimodal) which makes the data less reliable. Good to use with ordinal data. It is generally unaffected by anomalies and so safer to use with extreme values.