what is standard deviation and how is it done ?

Answer 1

Standard deviation of a population of data is the square root of variance; where variance = V = Sum[(x - m)^2]/N. x is each data point value in a database of N data points, and m is the weighted average of those N data points. For example:

If x = 1,2,3,4,5; the weighted average is the Sum(x)/N = 15/5 = 3 = m; so that V = [(1-3)^2 + (2-3)^2 + (3-3)^2 + (4-3)^2 + (5-3)^2]/5 = (4 + 1 + 0 + 1 + 4)/5 = 2.0 and Std Dev. = sqrt(V) = sqrt(2) = 1.414

A Std. Dev. is a measure of how spread out the data are. Bigger Std. Dev. means a wider range of data; smaller SD means the data are bunched up closer together.

In some applications, Std. Dev. is used to measure risk. For example, a stock price having a large SD will be more risky than a similar stock with a smaller SD. This results because, a widely swinging stock price could go waaaaay down and you could lose your shirt. A narrowly swinging stock price is less likely to tank; so you would be at less risk of losing your shirt.

Before I leave you, you should note that a "population" of data does not mean data about people necessarily. In statistics, a population simply means all the data that was collected. In the example I gave above, there were a total of five data points...no more, no less. Therefore, those five data points made up the population of that data.

Sometimes you have more data than you can handle; in which case you would select a small portion of the population to work with. That small portion of the population is called a sample. It's like a box of chcolates, you are watching your diet; so you can't eat them all. Thus, you take just a couple out of the box to sample them...the box is the population.

Even sampled data has a Std. Dev. The hope is that when we calculate a SD from a sample, that sample SD will be close to the SD for the whole population. That is, we infer the population SD from the value we get for the sample SD. There are sampling procedures and statistics that make this similarity between the sample and the population likely. But these are beyond the scope of this answer.

PS: I should add, standard deviation does not need a Bell/Normal curve to exist. In the example above, I made no such assumption; in fact, I have no clue what the example's distribution is. Even so, the SD = 1.414 is valid and a measure of spread of the five data points given.

If the data were Bell/Normal curve, however, we could make some probability statements based on the SD that cannot be made with other kinds of distribution. For example, if the data were Bell/Normal, we could say that about 2/3 of all the data points would fall randomly within the range from 3 - 1,414 to 3 + 1.414 or approsimate from 1.6 to 4.4. We can't say something like that if the data are not Bell/Normal shaped.

Answer 2

It's out of the bell shaped curve. Consult your textbook for formula.

Answer 3

what he said