# Standard Deviation explaination

1. May 29, 2004

### Elkay

I was given an assignment dealing with finding standard deviation. From the example given, I was able to do the assignment and get the correct answers, but I still don't understand standard deviation or its importance.

Could someone explain standard deviation to me, or at least point me to a good site that can explain the concept? Thanks.

2. May 29, 2004

### AKG

Standard deviation is supposed to given an idea of how far apart the data are from each other. For example, let's say you score a 50, 75, and 100 on three tests. Your average will be 75, but your standard deviation will be quite high. If you score 76, 74, 75, then your average is still 75, but your s.d. is much lower. Standard deviation, you could say, gives you an idea of the consistency or precision. Also, in an experiment, you expect to have a normal distribution of data. Now, in all normal curves, between 3 standard devations of the mean (so between $\bar x - 3\sigma$ and $\bar x + 3\sigma$) you expect about 99% of the data, between 2 s.d. you expect about 95%, and between 1 s.d. you expect something like 68%. So, it's a good way to see if your data matches a normal distribution.

The standard deviation is also used as a statistical measure of error. Like I mentioned, it measures precision. If your data is really spread apart (imprecise) then the s.d. will tell you that, and so when reporting your mean experimental value, you might have to report a high error because of the imprecise nature of your data.

I'm sure there are many other uses of the standard deviation.

There is a wikipedia article you may want to check out, and I'm sure you can do some searching on the net to find more info. If you want, here is the site I was given in my Physics Lab to understand how to deal with error, and there is some discussion on Gaussian/Normal curves, standard deviation, etc.

3. May 29, 2004

### Dooga Blackrazor

Here's how we were taught Standard Deviation:

2.5,13.5,34,average,34,13.5,2.5 (The % of each line on the bell curve graph)

You have a set of numbers. Lets say they are. (3,4,6,7,10)

1. First you add them all and divide to find the average. The average is 6 which would be your middle number or middle point of the graph. So for the sample of 5 students you average # is 6. Then you need to find standard deviation to find other sections.

2. Next you take all your numbers and subtract then by 6 which was your average.
(3,4,6,7,10) You now have, (-3,-2,0,1,4)

3. Then you square your new #'s. 9,4,0,1,16

4. Find the average of your new set of numbers. = 20. Divided 5 is 4.

5. Take the square root of your average of the squares. Which would be 2. Your Standard Deviation is two.

Therefore your bell graph is divided into:

2.5% - 13.5% - 34% - Average - 34% - 13.5% - 2.5%
0 - 2 - 4 - 6 - 8 - 10 - 12
You add or subtract your SD from your average. Your lines on the bell graph would be the percentages and the numbers.

If you want to now from the set of 5 numbers how often your above average you'd add all your percentages from the average and get 50%. If you wanted to know how many students got above 10 you'd look at your graph and find the answer to be 2.5%.

I hope that helped you somewhat. Different places and teachers probably explain SD differentially. If you have specific questions I can try and solve them for you.

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