Average and variance of salary/month
The story started with variance, I should have told you also another important concept --- average.

If you heard a company A's average salary for a month is 25,500 Euro, you might interested in to join the company. But, this company has only two people, a president and an employee. The president gets 50,000 Euro/month, and the employee gets 1,000 Euro/month. Now you see how average can deceive you. A company B is also two people company, but the president gets 30,000 Euro/month and the employee gets 21,000 Euro/month.

CompanyA

salary of president 50,000 Euro/month

salary of employee 1,000 Euro/month

Average of salary 25,500 Euro/month

CompanyB

salary of president 30,000 Euro/month

salary of employee 21,000 Euro/month

Average of salary 25,500 Euro/month

The averages are the same! If I can choose one of them as an employee, I will choose B. But, if they can provide only average, I can not see the difference. That's bad!

Therefore, statistics considers the squared average of difference from the average. (Oh, well, shall I put an equation here?) This is like putting how much difference from the average on a seesaw. If this is small, then everyone is close to the average like company B. You can consider this value as how much you can trust the average. If the value is large, then, someone is far from the average, means company A condition happens. If you want to know about the detail of this equation, look up ``variance'' or ``standard deviation'' in Google. I just compute the standard deviation of these salary/month here.

Company A

salary of president 50,000 Euro/month

salary of employee 1,000 Euro/month

Average of salary 25,500 Euro/month

Standard deviation 27,300

CompanyB

salary of president 30,000 Euro/month

salary of employee 21,000 Euro/month

Average of salary 25,500 Euro/month

Standard deviation 3,180

The averages are the same for the both companies, but, B is less dispersion, therefore, standard deviation becomes smaller than A. The average didn't give us this information. We use the variance or standard deviation in statistics because of this. We conventionally use σ as deviation. Now you know why we talk about σ.

Now you may see average deceits you. But of course average is important. With standard deviation (or variance) you can see more. This is the reason statistics uses standard deviation.