MERITS AND DEMERITS OF MEAN,MEDIAN,MODE,GM,HM AND WHEN TO USE THEM

MERITS AND DEMERITS OF MEAN,MEDIAN,MODE,GM,HM AND WHEN TO USE THEM .
STATISTICS
STATISTICAL METHIDS,
MEASURES OF CENTRAL TENDENCY,
ARTHMETIC MEAN

1. MERITS & DEMERITS OF MEAN,MEDIAN,MODE,GM,HM WHEN TO USE THEM

2. MEAN MERITS DEMERITS ·             It is easy to compute and has a unique value.  ·             It is based on all the observations.  ·             It is well defined.  ·             It is least affected by sampling fluctuations.  ·             It can be used for further statistical analysis. ·             The mean is unduly affected by the extreme items (outliers).  ·             It cannot be determined for the qualitative data such as beauty, honesty etc.  ·             It cannot be located by observations on the graphic method.

3. WHEN TO USE MEAN ?   Arithmetic mean is a best representative of the data if the data set is homogeneous. On the other hand if the data set is heterogeneous the result may be misleading and may not represent the data.

4. MEDIAN MERITS ·             It is easy to compute. It can be calculated by mere inspection and by the graphical method ·             It is not affected by extreme values. ·             It can be easily located even if the class intervals in the series are unequal DEMERITS ·             It is not amenable to further algebraic treatment ·             It is a positional average and is based on the middle item ·             It does not take into account the actual values of the items in the series

5. WHEN TO USE MEDIAN ?? The median is generally used to return the central tendency for skewed number distributions. Median is used to find middle most data. It is used to determine a point from where 50% of data is more & 50% data is less. It is used where extreme cases can be ignored. 

6. MODE MERITS ·             It is comparatively easy to understand. ·             It can be found graphically. ·             It is easy to locate in some cases by inspection. ·             It is not affected by extreme values. ·             It is the simplest descriptive measure of average DEMERITS ·            It is not suitable for further mathematical treatment. ·            It is an unstable measure as it is affected more by sampling fluctuations. ·            Mode for the series with unequal class intervals cannot be calculated. ·            In a bimodal distribution, there are two modal classes and it is difficult to determine the values of the mode . .

7. with categorical, ordinal, and discrete data. In fact, the  mode  is the only measure of central tendency that you can  use with  categorical data—such as the most preferred flavor of ice cream. However, with categorical data, there isn't a central value because you can't order the groups. WHEN TO USE MODE ??

8. HARMONIC MEAN MERITS ·             It is rigidly defined ·             It is based on all the observations of the series ·             It is suitable in case of series having wide dispersion ·             It is suitable for further mathematical treatment ·             It gives less weight to large items and more weight to small items DEMERITS ·             It is difficult to calculate and is not understandable ·             All the values must be available for computation ·             It is not popular due to its complex calculation. ·             It is usually a value which does not exist in series  

9. WHEN TO USE HM ?   Harmonic mean is used to calculate the average value when the values are expressed as value/unit. Since the speed is expressed as km/hour, harmonic mean is used for the calculation of average speed.   Relationship among the averages: In any distribution when the original items are different the A.M., G.M. and H.M would also differ and will be in the following order:   A.M. ≥ G.M ≥ H.M

10. GEOMETRIC MEAN MERITS ·             It is based on all the observations ·             It is rigidly defined ·             It is capable of further algebraic treatment ·             It is less affected by the extreme values ·             It is suitable for averaging ratios, percentages and rates. DEMERITS ·             It is difficult to understand ·             The geometric mean cannot be computed if any item in the series is negative or zero. ·             The GM may not be the actual value of the series ·             It brings out the property of the ratio of the change and not the absolute difference of change as the case in arithmetic mean.

11. WHEN TO USE GM ?   Geometric mean is used in calculations involving growth, investment, determination  of surface areas and volume.