Question

what is arithmetic mean? Mention two merits and demerits m​

Answer 1

The arithmetic mean, also called the average or average value, is the quantity obtained by summing two or more numbers or variables and then dividing by the number of numbers or variables. The arithmetic mean is important in statistics.

(A) Merits:

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.

(B) Demerits or Limitations:

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.

Answer 2

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ARITHMETIC MEAN :-  Arithmetic mean is the average of all the items.

Arithmetic mean is that value, which we get when we divide the sum of all the values of the items of a series with their total number.

ARITHMETIC MEAN IS OF TWO TYPES :

• Simple arithmetic mean.

• Weighted arithmetic mean.

FORMULA OF ARITHMETIC MEAN :-

• X ( bar ) = ∑X/N.

$\huge{\boxed{\sf{MERITS\:OF\:ARITHMETIC\:MEAN}}}$

• Arithmetic mean is simplest ans easiest one of all mean. It is easy to understand and also easy to calculate.

• Arithmetic mean is a definite number not an estimate.

• Arithmetic mean has various algebraic features so that it is used in higher statistical analysis.

$\huge{\boxed{\sf{DEMERITS\:OF\:ARITHMETIC\:MEAN}}}$

• Affected by extreme values.

• Do not represent all value all the times.

• Unnatural conclusions.

• Unsuitability.

• Wrong conclusion.