How are the measure of central tendency and measure of dispersion complementary to each other in describing data?
By explaining two distinct aspects of the data, the center and how data points gather.
On one hand, a measure of central tendency indicates the center 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 center of the distribution of data, and we have a good idea of how widely the data dispersed.