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This question already has an answer here:

Why we need variance in this world?

What is the purpose to make such function and how does it work?

I know that it is a measure of how the data spread, but why we don't just use the absolute variation to solve this problem?

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marked as duplicate by gung♦, Peter Ellis, Peter Flom♦, whuber♦ Apr 28 '13 at 13:43

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

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    $\begingroup$ Does this thread: Why square the difference instead of taking the absolute value in standard deviation answer your question? If there is anything you still want to know after reading that, please edit to clarify, otherwise this may need to be closed as a duplicate. On a slightly different topic, the reason for paying attention to the variance instead of just the SD, is because the variance is the parameter in the normal distribution, not the SD. E.g, variances add, but SDs don't. $\endgroup$ – gung♦ Apr 26 '13 at 22:27
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Or: Why do we need watermelons if we have rib eye steaks?

They are different things. There are many measures of dispersion which provide information about different features of a distribution.

A single number hardly summarises all the information about the shape of a distribution.

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