Standard deviation

[ben andrews' girlfriend]

Can someone explain it to me - idiot style? I need to know why we use it, what's it for, and how to work it out!!!


I'm meant to understand it, and i dont have a scooby!!!!

 

[robbied69]

So you can manipulate figures and say that you are XX% certain of something happen.

It is quite pointless as you can use figures to lie whichever way you wish.

 

[The Large One]

Standard Deviation

Lower case sigma means 'standard deviation'.
Capital sigma means 'the sum of'.
x bar means 'the mean'

The standard deviation measures the spread of the data about the mean value. It is useful in comparing sets of data which may have the same mean but a different range. For example, the mean of the following two is the same: 15, 15, 15, 14, 16 and 2, 7, 14, 22, 30. However, the second is clearly more spread out. If a set has a low standard deviation, the values are not spread out too much.

Example:
Find the standard deviation of 4, 9, 11, 12, 17, 5, 8, 12, 14
First work out the mean: 10.222
Now, subtract the mean individually from each of the numbers in the question and square the result. This is equivalent to the (x - xbar)² step. x refers to the values in the question.

x 4 9 11 12 17 5 8 12 14
(x - x)² 38.7 1.49 0.60 3.16 45.9 27.3 4.94 3.16 14.3

Now add up these results (this is the 'sigma' in the formula): 139.55
Divide by n-1. n is the number of values, so in this case is 8: 17.44
And finally, square root this: 4.18

The standard deviation can usually be calculated much more easily with a calculator and this is usually acceptable in exams. With some calculators, you go into the standard deviation mode (often mode '.'). Then type in the first value, press 'data', type in the second value, press 'data'. Do this until you have typed in all the values, then press the standard deviation button (it will probably have a lower case sigma on it). Check your calculator's manual to see how to calculate it on yours.

NB: If you have a set of numbers (e.g. 1, 5, 2, 7, 3, 5 and 3), if each number is increased by the same amount (e.g. to 3, 7, 4, 9, 5, 7 and 5), the standard deviation will be the same and the mean will have increased by the amount each of the numbers were increased by (2 in this case).

When dealing with data such as the following:
x f
4 9
5 14
6 22
7 11
8 17

the formula for standard deviation becomes:







Try working out the standard deviation of the above data. You should get an answer of 1.32 .

 

[Hiney]

Nor me but have a look at this. Don't know if it will help

Standard Deviation

 

[Trufflehound]

I'd suggest askng Kinky, but he only seems to know about sub-standard deviation.

 

[Lord Bracknell]

I assume you've had no help from North Stand Polls, where they seem to understand the full range of deviations.

Try this site:-

http://www.robertniles.com/stats/stdev.shtml

I can honestly say that I never understood the concept when it was first explained to me as part of a University statistics course, nor did it make any sense when - fifteen years later - my employer spent a fortune on packing me off to a residential course at Cranfield University, which included an otherwise comprehensible statistics module.

But, after a lifetime of playing around with data and assembling statistical reports for councillors and fellow transport professionals, I can report that ...

... I have NEVER been pulled up on my ignorance of what the hell it is all about.

And that's because no-one - even those who have heard of the concept - likes to admit that that they DON'T KNOW WHAT IT MEANS.

 

[Faldo]

Standard Deviation - derived from greek terminology meaning BUNCH OF ARSE!

 

[ben andrews' girlfriend]

Standard Deviation - derived from greek terminology meaning BUNCH OF ARSE!

That's as far as i got in the lecture - when i gave up and started to think of what im going to eat when i got home!

 

[¤DãŃn¥ §êãGüLL¤]

Standard Deviation

Lower case sigma means 'standard deviation'.
Capital sigma means 'the sum of'.
x bar means 'the mean'

The standard deviation measures the spread of the data about the mean value. It is useful in comparing sets of data which may have the same mean but a different range. For example, the mean of the following two is the same: 15, 15, 15, 14, 16 and 2, 7, 14, 22, 30. However, the second is clearly more spread out. If a set has a low standard deviation, the values are not spread out too much.

Example:
Find the standard deviation of 4, 9, 11, 12, 17, 5, 8, 12, 14
First work out the mean: 10.222
Now, subtract the mean individually from each of the numbers in the question and square the result. This is equivalent to the (x - xbar)² step. x refers to the values in the question.

x 4 9 11 12 17 5 8 12 14
(x - x)² 38.7 1.49 0.60 3.16 45.9 27.3 4.94 3.16 14.3

Now add up these results (this is the 'sigma' in the formula): 139.55
Divide by n-1. n is the number of values, so in this case is 8: 17.44
And finally, square root this: 4.18

The standard deviation can usually be calculated much more easily with a calculator and this is usually acceptable in exams. With some calculators, you go into the standard deviation mode (often mode '.'). Then type in the first value, press 'data', type in the second value, press 'data'. Do this until you have typed in all the values, then press the standard deviation button (it will probably have a lower case sigma on it). Check your calculator's manual to see how to calculate it on yours.

NB: If you have a set of numbers (e.g. 1, 5, 2, 7, 3, 5 and 3), if each number is increased by the same amount (e.g. to 3, 7, 4, 9, 5, 7 and 5), the standard deviation will be the same and the mean will have increased by the amount each of the numbers were increased by (2 in this case).

When dealing with data such as the following:
x f
4 9
5 14
6 22
7 11
8 17

the formula for standard deviation becomes:







Try working out the standard deviation of the above data. You should get an answer of 1.32 .

That's what I thought.

 

[Gritt23]

The standard deviation is the amount of variation you would expect from the mean (average), in say 98% of the time.

It means that in the vast majority of time the actual result will be within the standard deviation of the mean, so within those boundaries.

 

[Seagullible]

The standard deviation is the amount of variation you would expect from the mean (average), in say 98% of the time.

It means that in the vast majority of time the actual result will be within the standard deviation of the mean, so within those boundaries.

Well put. It's an odd thing cos it's like the average mark away from the average

 

[tricky]

To try and put it into context:-
You have a 'true' mean and the mean of the population that you are looking at, the standard deviation explains the variance of that sample population mean.
Obviosuly the more data you have in your sample population, the more you know about the true population and the less variance there is and so the standard deviation is smaller.
It's very important in statistics as it allows you to judge whether the inferences you extract from the data are actually at all relevant to the real data.

Does that help.

 

[dwayne]

It makes sense to me

think of it as the mean of the mean. Also think of WHY you are using it...it is generally only a feasible measurement when the group of numbers that you are looking at are largely distributed, hence scewing the overall mean.

 

[ben andrews' girlfriend]

It makes sense to me

Well it should, working where you do

 

[ben andrews' girlfriend]

To try and put it into context:-
You have a 'true' mean and the mean of the population that you are looking at, the standard deviation explains the variance of that sample population mean.
Obviosuly the more data you have in your sample population, the more you know about the true population and the less variance there is and so the standard deviation is smaller.
It's very important in statistics as it allows you to judge whether the inferences you extract from the data are actually at all relevant to the real data.

Does that help.

Most of it does

*runs off to buy Statistics for dummies*

 

[dwayne]

Well it should, working where you do

xx

 

[Simster]

It makes sense to me

think of it as the mean of the mean. Also think of WHY you are using it...it is generally only a feasible measurement when the group of numbers that you are looking at are largely distributed, hence scewing the overall mean.

Kind of, though not the mean of the mean. It's a measure of average distance away from the mean.


So:

16, 20, 24 have a mean of 20.
10, 12, 38 have a mean of 20, but a much higher standard deviation.

Here's an example of it's use:

Leyton Orient have three home games, that are watched by crowds of 4,073 4,100 and 7,554 giving them an average gate of 5,242.
Over the same period, the mighty stripes might have had gates of 5,954, 5,833 and 5,922 - an average crowd of 5903

Now on the face of it, you can't tell a big difference between the mighty stripes and the two bob shower of shit from the arse end of London by simply checking the two mean gates. However the tiny standard deviation of our gates suggests a greater fanbase loyalty or a ceiling on capacity. A closer look at the much higher standard deviation on Orient's 3 gates would suggest two tiny piddly laughable gates befitting a non league outfit and a single one-off bumper home crowd. Obviously the day when we took over the place.

 

[Dick Knights Mumm]

You're the man Simster.

I think I understand standard deviation now.

 

[ben andrews' girlfriend]

Thanks Simster - it makes so much more sense now!!!

 

[WATFORD zero]

Simster, you've missed you're calling

You should get a career teaching new things to young ladies