How are the measures of central tendency and measures of dispersion complementary?

Feb 13, 2018

Explanation:

Measures of central tendency are mean, mode and median. Even we have three types of mean, such as arithmatic mean, geometric mean and harmonic mean.

They tell us the central value around which the data is distributed. For example consider the data set $6 , 8 , 2 , 4 , 12 , 5 , 8 , 10 , 3 , 4$. In this sum of numbers is $62$ and as they are ten in number, mean is $\frac{62}{10} = 6.2$

Note that smallest number is $2$ and largest number is $12$. Now, even if we had set of numbers as $5 , 6 , 7 , 5 , 8$ and as sum of numbers is $31$ and they are five, mean is still $\frac{31}{5} = 6.2$. But $5 , 6 , 7 , 5 , 8$ are far more narrowly spread and hence nature of data is not very well brought out by just mean.

Similarly, we can have two data sets with same median or mode, but their spread may be different, as mode is just the more frequent among data points and median is the value of central data point, when the samme is arranged in increasing or decreasing order.

Measures of dispersion tell us better about the kind of spread. In a way, mean deviation or standard deviation tell us more about the way data is spread.

For example, data set $30 , 40 , 50 , 60 , 70$ and data set $10 , 30 , 50 , 70 , 90$ have same mean, mode and median but while mean deviation of first data set is $12$, that of second data set is $24$, indicating that second data set is too wide spread.

What about two data sets $30 , 40 , 50 , 60 , 70$ and $130 , 140 , 150 , 160 , 170$? Their mean deviation is same i.e. $12$, but are they not widely different as mean of first data set is $50$, while that of second data set is $150$.

It is obvious that measures of central tendency and measures of dispersion are both important and complementary.