MERITS AND DEMERITS OF ARITHEMETIC MEAN

ARITHEMETIC MEAN RIGIDLY DEFINED BY ALGEBRIC FORMULA It is easy to calculate and simple to understand IT BASED ON ALL OBSERVATIONS AND IT CAN BE REGARDED AS REPRESENTATIVE OF THE GIVEN DATA It is capable of being treated mathematically and hence it is widely used in statistical analysis. 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. It is least affected by the fluctuation of sampling

DEMERITS OF ARITHMETIC MEAN It

can neither be determined by inspection or by graphical location Arithmetic mean cannot be computed for qualitative data like data on intelligence honesty and smoking habit etc It is too much affected by extreme observations and hence it is not adequately represent data consisting of some extreme point Arithmetic mean cannot be computed when class intervals have open ends

MERITS OF MEDIAN It

is easy understand and to easy to calculate It can easy to find out by inspection Median can be determined even when class intervals have open ends It is not much affected by extreme observations and also interdependent of range or dispersion of the data Median can also be located graphically It is only suitable average when the data are qualitative & it is possible to rank various items according to qualitative charecteristics

Merits of mode It

is easy to understand and easy to calculate. In many cases it can be located just by inspection Like mean or median it is not affected by extreme observations It can be determined even if distribution has open end classes It is value around which more concentrations of observations and hence the best representative of data

Demerits of mode It

is not based on all observations It is not capable of further mathematical treatment It is much affected by fluctuations of sampling It is not suitable when different items of data are unequal impotance

Merits and demerits of range It

is easy to understand and easy to calculate It gives quick measure of variability DEMERITS It is not based on all observations it is very much affected by extreme observations It is only gives rough idea of spread of observations It cannot to be calculated for a distributions with open ends

Merits and demerits of standard deviationMERITS 1)It is a rigidly defined measure of dispersion 2)It is based on all the observations 3)It is capable of being treated mathematically. For example, if standard deviations of a number of groups are known, their combined standard deviation can be computed 4)It is not very much affected by the fluctuations of sampling and therefore is widely used in sampling theory and test of significance DEMERITS 1)As compared to the quartile deviation and range etc, it is difficult to understand and difficult to calculate 2)It gives more importance to extreme observation 3)Since it depends upon the units of measurement of the observations, it cannot be used to compare the dispersion of the distribution expressed in different units

. USES OF STANDARD DEVIATIONStandard deviation can be used to compare the dispersions of two or more distributions when their units of measurements and arithmetic means are same It is used to test the reliability of mean. it may be pointed out here that the mean of a distribution with least standard deviation is said to be more reliable.

DEMERITS OF MEDIAN In

case of individual observations the process of locations of median requires their arrangement in order of the magnitude which may be cumbersome task It is being a positional average it is not capable treated algebraically It not based on the magnitude of all the observations in comparison to arithmetic mean it much affected by the fluctuations of sampling