Mean Median Mode


Statistics / Friday, August 10th, 2018

Advantages and Disadvantages of Mean Median Mode

Here we will get to know about the advantages and disadvantages of mean median mode. Consider the disadvantages as limitations of mean, median, and mode. Sometimes questions are asked to write the merit and demerit of mean, median and mode which is same, we are discussing here.

Mean(AM, GM, HM):

Mean is the average of all the values of the given series. Mean are of three types, they are Arithmetic Mean, Geometric Mean and Harmonic mean. Following are the rules of calculations of them respectively:

\[\overline{X}=\frac{{{x}_{1}}+{{x}_{2}}+{{x}_{3}}+…+{{x}_{n}}}{n}=\frac{\sum\limits_{i=1}^{n}{{{x}_{i}}}}{n}\]

\[GM=anti\log (\frac{\sum{\log x}}{n})\]

\[HM=\frac{n}{\sum{\frac{1}{{{x}_{i}}}}}\]

Advantages / Merits:
It is simple to calculate and easy to understand.
Is based on all values.
It is compactly defined.
Mean is quite more stable.

Disadvantages / Demerits:
It is affected by extreme values.
It cannot be determined for distributions with open-end class intervals.
Cannot be graphically located.
Sometimes it is a value which is not in the series.

Median:

Median is the middle value of the series when the series is sorted in ascending or descending order.

Advantages / Merits:
It can be easily understood and computed.
It is not affected by extreme values.
Median can be determined by Ogives (graphically).

Disadvantages / Demerits:
It is not based on all values.
Is not capable of further algebraic treatment.

Mode:

Mode is the value which has the maximum frequency in the series.

Advantages / Merits:
In many cases, it can be found by inspection.
It is not affected by extreme values.
Can be calculated for distributions with open end classes.
Mode can be located graphically.
It is used for qualitative data.

Disadvantages / Demerits:
It is not based on all values.
Is not capable of further mathematical treatment.
Mode is much affected by sampling fluctuations.

Relation among Mean Median Mode

Mean – Mode = 3 (Mean – Median) which is same as, Mode = 3 Median – 2 Mode

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