What is a standard deviation and what does it means?

Question

What is a standard deviation and what does it means?

Answer 1

Standard deviation is a measure of the "spread" or range of values in a collection of data. Two sets of data can have the same average value, yet be very different in nature. If most of the values are close to the average "deviating" only a little from that, the standard deviation is small. If many values are very different from the average, the standard deviation is large. If you were to take a sample from a collection of data, it is more likely to be near the average in value if the standard deviation of that collection is small.

For a more technical explanation and specific formulas see http://en.wikipedia.org/wiki/Standard_deviation

Answer 2

You can think of it as being the average deviation from the mean. Take a population, and look at one statistic. Say, the age of a group of people. They have a mean age of 30 years old. But you have people of all ages, and you wonder how your group is distributed over their range; so you look at what is, on average, how much older or younger than the mean the people in the group are.
It is useful to know that, because with just the mean and the standard deviation, you have a pretty good idea how the whole population is distributed. And that is required to design things like the size of chairs; you would want it the be comfortable for, say, 99% of the population. So, you can deduct, from the standard deviation, what is the height that 99% of the population is smaller or equal to. Those that are very tall will not be comfortable in your chair and would need custom design, but those are only 1% of the population, a very small number of potential customers, however your chairs that are meant for the 99% of the population can be made cheaper as they will be made in great quantity.