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

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pompatzz8 · Accepted Answer

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.

How are the measures of central tendency and measures of

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