Why do we need the Variance when we already have the Mean?

The roles played by Mean and Variance are different but complementary. Mean gives the average value of data whereas Variance gives the spread of data. So as a manufacturer if we are interested in the quality of product then mean on one hand gives the average quality. The variance on the other hand gives the consistency of this quality. But these measures can also be used in depth analysis, resulting in wider generalization of results obtained from the sample to the whole population. This concept can be explained by following example.

Average life expectancy or average longevity in years is a development indicator of any country. For a developed country these take higher values in comparison to a developing country. For example average life expectancy of a Nepalese in 2012 was 67 years, whereas average life expectancy of Japanese in 2012 was 83 years. Higher average value for Japan in contrast to that of Nepal reflects higher standard of living in Japan with good health care facilities offered by the government. The variance in the longevity of an individual from the average value will be smaller in Japan, implying that there is not much difference in the longevity with respect to the average value. So for a developed country the average is high and the variance (from mean 83 years) is low, as many individual live till 83 years. But for Nepal the average is low and the variance (from the mean 67 years) is high, as many die in their late fifties and many live till their seventies.