# What is standard deviation?

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I've tried to understand loads but don't quite get it. Is it the average distance a point is from the mean? (If its not the mean)

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#2

It's the mean distance the points are from the theoretical mean. More simply put, it's just a measure of how spread out data is.

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#3

(Original post by

I've tried to understand loads but don't quite get it. Is it the average distance a point is from the mean? (If its not the mean)

**MathsMeister**)I've tried to understand loads but don't quite get it. Is it the average distance a point is from the mean? (If its not the mean)

It's one of a number of so-called "measures of dispersion" i.e. things which tell you how spread out your data are. Other examples are things like range and inter-quartile range.

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I thouught that if its how spread out the data points are then it's be the mean of how far out the values which are spread are spread out. But then the ones with negative deviations should be made positive so not to make zero. But then he squares the numbers to do that instead, which makes no sense let alone square rooting it.

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#5

(Original post by

I thouught that if its how spread out the data points are then it's be the mean of how far out the values which are spread are spread out.

**MathsMeister**)I thouught that if its how spread out the data points are then it's be the mean of how far out the values which are spread are spread out.

But then the ones with negative deviations should be made positive so not to make zero. But then he squares the numbers to do that instead, which makes no sense let alone square rooting it.

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#6

(Original post by

Didn't you cover this at GCSE

**davros**)Didn't you cover this at GCSE

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#7

(Original post by

SD is not in the standard GCSE

**TenOfThem**)SD is not in the standard GCSE

http://www.mathsrevision.net/gcse-ma...dard-deviation

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#9

It's not a topic for GCSE Maths but it is for GCSE Statistics, a similar thing.

But as others have said, standard deviation is a measure of spread

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But as others have said, standard deviation is a measure of spread

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why can you not just make the distance from the mean positive and add the distances up and divide by how many?

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#11

(Original post by

why can you not just make the distance from the mean positive and add the distances up and divide by how many?

**MathsMeister**)why can you not just make the distance from the mean positive and add the distances up and divide by how many?

However - let's say that you have 10000 values - do you really think it would be a good idea to work out each difference, check if it were negative and if so multiply by -1 prior to adding all of the values

The squaring, summing, rooting avoids this

As with anything in maths this is a constructed value rather than anything that occurs "naturally"

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#12

(Original post by

SD is not in the standard GCSE

**TenOfThem**)SD is not in the standard GCSE

I thought GCSE was loaded up with more stats than ever before (and we certainly did SD for O level). What on earth do they find to cover in the stats component of GCSE?

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#13

**MathsMeister**)

why can you not just make the distance from the mean positive and add the distances up and divide by how many?

There isn't a unique measure of spread, and many mathematicians have argued for the use of MAD instead of SD. However, the formula relies on using modulus signs rather than squares and square roots which makes things more difficult when you come to work out properties of distributions by doing things like differentiation.

SD is largely a historical choice, through looking at things like the normal distribution and analysis of regression lines and minimizing errors.

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#14

(Original post by

That would be fine if you had 10 values for example

However - let's say that you have 10000 values - do you really think it would be a good idea to work out each difference, check if it were negative and if so multiply by -1 prior to adding all of the values

The squaring, summing, rooting avoids this

As with anything in maths this is a constructed value rather than anything that occurs "naturally"

**TenOfThem**)That would be fine if you had 10 values for example

However - let's say that you have 10000 values - do you really think it would be a good idea to work out each difference, check if it were negative and if so multiply by -1 prior to adding all of the values

The squaring, summing, rooting avoids this

As with anything in maths this is a constructed value rather than anything that occurs "naturally"

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#15

(Original post by

Really????

I thought GCSE was loaded up with more stats than ever before (and we certainly did SD for O level). What on earth do they find to cover in the stats component of GCSE?

**davros**)Really????

I thought GCSE was loaded up with more stats than ever before (and we certainly did SD for O level). What on earth do they find to cover in the stats component of GCSE?

"How much TV do you watch ?"

ii) "Yim Wah has 5 red balls and 3 green balls. What is the chance she picks a yellow ball ?"

iii) Look at the cumulative frequency curve opposite. If the mark for an A* is 32% estimate the proportion of students who go an A* "

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#16

(Original post by

i) "What is wrong with Ahmed's survey question:

"How much TV do you watch ?"

ii) "Yim Wah has 5 red balls and 3 green balls. What is the chance she picks a yellow ball ?"

iii) Look at the cumulative frequency curve opposite. If the mark for an A* is 32% estimate the proportion of students who go an A* "

**the bear**)i) "What is wrong with Ahmed's survey question:

"How much TV do you watch ?"

ii) "Yim Wah has 5 red balls and 3 green balls. What is the chance she picks a yellow ball ?"

iii) Look at the cumulative frequency curve opposite. If the mark for an A* is 32% estimate the proportion of students who go an A* "

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#17

(Original post by

Sadly I suspect these questions will turn up one day. Statistics can be uninspiring enough without the sort of nonsense being taught today, but there seems to be no real impetus to change things.

**davros**)Sadly I suspect these questions will turn up one day. Statistics can be uninspiring enough without the sort of nonsense being taught today, but there seems to be no real impetus to change things.

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#18

**davros**)

Really????

I thought GCSE was loaded up with more stats than ever before (and we certainly did SD for O level). What on earth do they find to cover in the stats component of GCSE?

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So there isn't another way of doing it without the outliers being overweighted unless you do the mean absolute deviation. But then you wouldn't be able to do all those other things when differentiating as mentioned earlier? To me it doesn't make sense doing SD if it is not a true average.

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#20

(Original post by

So there isn't another way of doing it without the outliers being overweighted unless you do the mean absolute deviation. But then you wouldn't be able to do all those other things when differentiating as mentioned earlier? To me it doesn't make sense doing SD if it is not a true average.

**MathsMeister**)So there isn't another way of doing it without the outliers being overweighted unless you do the mean absolute deviation. But then you wouldn't be able to do all those other things when differentiating as mentioned earlier? To me it doesn't make sense doing SD if it is not a true average.

SD is just a measure of "spread" or "dispersion" (in more technical language) - there are others, as I've explained, but just not in common use.

Outliers are irrelevant - if you believe you have outliers then you exclude them from your analysis in the first place, whether you're calculating a measure of central tendency (like the mean) or a measure of dispersion (like range or SD).

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