What are Mean, Median, Mode? Explain its merits and demerits of them.
Answers
Mode
Type of average that refers to the most-common or most-frequently occurring value in a series of data. For example, the mode of the series 1, 2, 2, 3, 4, 4, 4, 5, 5, 6 is 4 because it is the only value occurring thrice. In any series there may or may not be a mode, or two modes (called bimodal series) or more modes (called multimodal series). In a frequency distribution graph, the peak represents the mode.The mode or modal value of a distribution is that value of the variable for which the frequency is maximum.The number which is repeated maximum number of times is the mode.
Merits->
1) It is readily comprehensible and easy to compute. In some case it can be computed merely by inspection.
2) It is not affected by extreme values. It can be obtained even if the extreme values are not known.
3) Mode can be determined in distributions with open classes.
4) Mode can be located on the graph also.
5) If all the data are not given then also mode can be calculated.
Demerits->
1) It is ill defined. It is not always possible to find clearly defined mode. In some cases, we may come across distributions with two modes. Such distributions are called Bimodal. If a distribution has more than two modes, it is said to be Multimodal.
2) It is not based upon all the observation.
3) Mode can be calculated by various formulae as such the value may differ from one to other. Therefore, it is not rigidly defined.
4) It is affected to a greater extent fluctuations of sampling.
Median
The median is the middle number in a group of numbers. It's not as commonly used as the others, but it can be the best 'average' to use when you have a set of data that contains outliers.Median is the middle value of the distribution i.e median of a distribution is the value of the variable which divides it into two equal parts. It is the value of the variable such that the number of observations above it is equal to the number of observations below it.
Merits->
1) It is easy to compute and understand.
2) It is well defined an ideal average should be.
3) It can also be computed in case of frequency distribution with open ended classes.
4) It is not affected by extreme values and also interdependent of range or dispersion of the data.
5) It can be determined graphically.
demerits->>
1) For computing median data needs to be arranged in ascending or descending order.
2) It is not based on all the observations of the data.
3) It can not be given further algebraic treatment.
4) It is affected by fluctuation of sampling.
5) It is not accurate when the data is not large.
Mean
The Arithmetic Mean is the average of the numbers: a calculated "central" value of a set of numbers.
Example: what is the mean of 2, 7 and 9?
Add the numbers: 2 + 7 + 9 = 18
Divide by how many numbers (i.e. we added 3 numbers): 18 ÷ 3 = 6
So the mean is 6
Merits->
1) Arithmetic mean rigidly defined by Algebraic Formula.
2) It is easy to calculate and simple to understand.
3) It is based on all observations of the given data.
4) It is capable of being treated mathematically hence it is widely used in statistical analysis.
5) Arithmetic mean can be computed even if the derailed distribution is not known but some of the observation and number of the observation are known.
Demerits->>
1) It can neither be determined by inspection or by graphical location.
2) Arithmetic mean can not be computed for qualitative data like data on intelligence honesty and smoking habit etc.
3) It is too much affected by extreme observations and hence it is not adequately represent data consisting of some extreme point.
4) Arithmetic mean can not be computed when class intervals have open ends.
5) If any one of the data is missing then mean can not be calculated.
Hope this helps! ;)
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