Can anyone explain to me what standard deviation is in mathematics?

Question

I am failing my college statistics course and it is basically because I don't know how to compute the standard deviation. Somebody help me PLEASE!!!!

Answer 1

I think the first answer is wrong. Where it says divide by nine instead of ten, you should divide by ten.

Basically you are trying to estimate how much variation there is in a series of numbers. You first find the mean. You then find out how far each number is from the mean. You square each of these deviations (which will make them all positive so that a number that is -10 away from the mean and one that is +10 will both square to 100 since they are both the same distance from the mean). You then add them up and find the mean of the squared deviations. You then take the square root of this to find the standard deviation.

As an example, if you have two numbers, 1 and 9. Their mean is 5. [(1 + 9) / 2 = 5]

The differences are -4 and 4. [1 - 5 = -4, 9 - 5 = 4]

The the squares of these are both 16.

The mean of 16 and 16 is 16 and the square root of 16 is 4.

Thus, in this example, the standard deviation is the same as the actual deviation since we only had two data points.

If you add two more points, say 3 and 7, the average stays at 5.

The differences are now -4, -2, +2, and +4.

The squares of these differences are 16, 4, 4, and 16.

The average of these squares is 10 and the root is 3.16227766.

Note that the standard deviation of 3.16 is slightly more than the mean of the absolute values of the differences (which would be 3). This is because the standard deviation formula emphasizes the extremes.

Answer 2

"The standard deviation is the root mean square (RMS) deviation of the values from their arithmetic mean. For example, in the population {4, 8}, the mean is 6 and the standard deviation is 2. This may be written: {4, 8} ≈ 6±2. In this case 100% of the values in the population are at one standard deviation of the mean. Standard deviation is the most common measure of statistical dispersion, measuring how widely spread the values in a data set are. If the data points are all close to the mean, then the standard deviation is close to zero. If many data points are far from the mean, then the standard deviation is far from zero. If all the data values are equal, then the standard deviation is zero."

I found this from the encyclopedia, which you can go to:
http://en.wikipedia.org/wiki/Standard_deviation

Hope this will help you.

Answer 3

Suppose you have ten numbers.

Add them up and divide by ten. This new number is called the mean.

For each of the original numbers, subtract the mean, and with this new number, square the new number.

Add the squares, and divide by nine, not ten.

Take the square root.

That is the standard deviation.

Answer 4

the previous answerer did no longer answer the asker's first query: The pattern ordinary deviation is an estimate of the inhabitants's ordinary deviation. whilst the pattern length is small (n < 30) the estimate isn't seen terrific and statistical problems are solved, employing the t-distribution to compensate. If the pattern length is ? 30, and/or if the inhabitants ordinary deviation is ordinary, the z-distribution is used.