1.8 What are merits and demerits of Arithmetic
mean
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MERIT
1. It can be easily calculated; and can be easily understood. It is the reason that it is the most used measure of central tendency.
2. As every item is taken in calculation, it is effected by every item.
3. As the mathematical formula is rigid one, therefore the result remains the same.
4. Fluctuations are minimum for this measure of central tendency when repeated samples are taken from one and the same population.
5. It can further be subjected to algebraic treatment unlike other measures i.e. mode and median.
6. A.M. has also a plus point being a calculated quantity and is not based on position of terms in a series.
7. As it is rigidly defined, it is mostly used for comparing the various issues.
DEMERIT
1. It cannot be located graphically.
2. A single item can bring big change in the result. For example if there are three terms 4, 7, 10 ; X is 7 in this case. If we add a new term 95, the new X is 4+7+10+95/4 = 116/4 = 29. This is a big change as compared to the size of first three terms’ X- .
3. Its value will be effective only if the frequency is normally distributed. Otherwise in case skewness is more, the results become ineffective.
4. In case of open end class intervals we have to assume the limits of such intervals and a little variation in X can take place. Such is not the case with median and mode, and there is no use of the open end intervals in its calculations.
5. Qualitative forms such as Cleverness, Riches etc. cannot give X as data can’t be expressed numerically.
6. X cannot be located by inspection as in the case of mode and median.
7. Sometimes it gives impossible or laughable conclusions, e.g. if there are 60, 50 and 12 students in three classes then average number of students is 60+50+42/3 = 50.67, which is impossible as students can’t be in fractions.
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