Explain the merits and demerits of mean , median and mode
Answers
MERITS OF ARITHEMETIC MEAN
l ARITHEMETIC MEAN RIGIDLY DEFINED BY ALGEBRIC FORMULA
l It is easy to calculate and simple to understand
l IT BASED ON ALL OBSERVATIONS AND IT CAN BE REGARDED AS REPRESENTATIVE OF THE GIVEN DATA
l It is capable of being treated mathematically and hence it is widely used in statistical analysis.
l Arithmetic mean can be computed even if the detailed distribution is not known but some of the observation and number of the observation are known.
l It is least affected by the fluctuation of sampling
DEMERITS OF ARITHMETIC MEAN
l It can neither be determined by inspection or by graphical location
l Arithmetic mean cannot be computed for qualitative data like data on intelligence honesty and smoking habit etc
l It is too much affected by extreme observations and hence it is not adequately represent data consisting of some extreme point
l Arithmetic mean cannot be computed when class intervals have open ends
MERITS OF ARITHEMETIC MEAN
l ARITHEMETIC MEAN RIGIDLY DEFINED BY ALGEBRIC FORMULA
l It is easy to calculate and simple to understand
l IT BASED ON ALL OBSERVATIONS AND IT CAN BE REGARDED AS REPRESENTATIVE OF THE GIVEN DATA
l It is capable of being treated mathematically and hence it is widely used in statistical analysis.
l Arithmetic mean can be computed even if the detailed distribution is not known but some of the observation and number of the observation are known.
l It is least affected by the fluctuation of sampling
DEMERITS OF ARITHMETIC MEAN
l It can neither be determined by inspection or by graphical location
l Arithmetic mean cannot be computed for qualitative data like data on intelligence honesty and smoking habit etc
l It is too much affected by extreme observations and hence it is not adequately represent data consisting of some extreme point
l Arithmetic mean cannot be computed when class intervals have open ends
Lack of representative character: - Median fails to be a representative measure in case of such series the different values of which are wide apart from each other. Also, median is of limited representative character as it is not based on all the items in the series.
(2) Unrealistic:- When the median is located somewhere between the two middle values, it remains only an approximate measure, not a precise value.
(3) Lack of algebraic treatment: - Arithmetic mean is capable of further algebraic treatment, but median is not. For example, multiplying the median with the number of items in the series will not give us the sum total of the values of the series.
However, median is quite a simple method finding an average of a series. It is quite a commonly used measure in the case of such series which are related to qualitative observation as and health of the student.
(1) Simple and popular: - Mode is very simple measure of central tendency. Sometimes, just at the series is enough to locate the model value. Because of its simplicity, it s a very popular measure of the central tendency.
(2) Less effect of marginal values: - Compared top mean, mode is less affected by marginal values in the series. Mode is determined only by the value with highest frequencies.
(3) Graphic presentation:- Mode can be located graphically, with the help of histogram.
(4) Best representative: - Mode is that value which occurs most frequently in the series. Accordingly, mode is the best representative value of the series.
(5) No need of knowing all the items or frequencies: - The calculation of mode does not require knowledge of all the items and frequencies of a distribution. In simple series, it is enough if one knows the items with highest frequencies in the distribution.
Step-by-step explanation:
refer to the attachment above ❤
