Question

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

Answer 1

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

Complete step-by-step answer:
On one hand, a measure of central tendency indicates the centre of the data distribution; which is the value around which all the data points gather. But still, we do not know how closely data points gather around that value. It could be very tight, or it could be very loose. There is no way to tell by looking at the central tendency alone.
On the other hand, a measure of dispersion indicates how 'dispersed' the data points are around the central value. A higher measure of dispersion suggests data points gather loosely around the central value (highly dispersed), and conversely, a lower measure of dispersion suggests they gather tightly.
But looking at the dispersion measure alone does not tell us where the central value is. That is why, we need both measures of central tendency and dispersion, so that we know the centre of the distribution of data, and we have a good idea of how widely the data dispersed.

Note: It is obvious that measures of central tendency and measures of dispersion are both important and complementary. We can have two datasets with the same median or mode, but their spread may be different.