__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

__Median:__The median is that value of the series which divides the group into two equal parts, one part comprising all values greater than the median value and the other part comprising all the values smaller than the median value.

Merits of median

Merits of median

(1)

**It is very simple measure of the central tendency of the series. I the case of simple statistical series, just a glance at the data is enough to locate the median value.**

__Simplicity:-__(2)

__Free from the effect of extreme values:__**-**Unlike arithmetic mean, median value is not destroyed by the extreme values of the series.

(3)

**- Certainty is another merits is the median. Median values are always a certain specific value in the series.**

__Certainty:__(4)

**- Median value is real value and is a better representative value of the series compared to arithmetic mean average, the value of which may not exist in the series at all.**

__Real value:__(5)

**Graphic presentation:**__- Besides algebraic approach, the median value can be estimated also through the graphic presentation of data.__

(6)

**Possible even when data is incomplete:**__- Median can be estimated even in the case of certain incomplete series. It is enough if one knows the number of items and the middle item of the series.__

**Demerits of median:**

Following are the various demerits of median:

(1)

**- 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.**

__Lack of representative character:__(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.

**Mode:**

The value of the variable which occurs most frequently in a distribution is called the mode.

**Merits of mode:**

Following are the various merits of mode:

(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)

**- Compared top mean, mode is less affected by marginal values in the series. Mode is determined only by the value with highest frequencies.**

__Less effect of marginal values:__(3)

**Mode can be located graphically, with the help of histogram.**

__Graphic presentation:-__(4)

**- Mode is that value which occurs most frequently in the series. Accordingly, mode is the best representative value of the series.**

__Best representative:__(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.__

**Demerits of mode:**

Following are the various demerits of mode:

(1)

**- Mode is an uncertain and vague measure of the central tendency.**

__Uncertain and vague:__(2)

**- Unlike mean, mode is not capable of further algebraic treatment.**

__Not capable of algebraic treatment:__(3)

__Difficult:__**-**With frequencies of all items are identical, it is difficult to identify the modal value.

(4)

**- Calculation of mode involves cumbersome procedure of grouping the data. If the extent of grouping changes there will be a change in the model value.**

__Complex procedure of grouping__:(5)

**It ignores extreme marginal frequencies. To that extent model value is not a representative value of all the items in a series.**

__Ignores extreme marginal frequencies__:-Besides, one can question the representative character of the model value as its calculation does not involve all items of the series.