What is standard deviation?

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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(edited 9 years ago)

Reply 2

Original post by 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)

Didn't you cover this at GCSE (I'm asking cos I think you're starting A level now, not because I'm being funny!)?

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.

Reply 3

MathsMeister

OP

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.

Reply 4

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Original post by 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.

That is exactly what's happening, we're just choosing to measure from a central point (the mean)

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.

Perhaps you can elaborate, because I don't see the problem with that.

Reply 5

TenOfThem

Original post by davros

Didn't you cover this at GCSE

SD is not in the standard GCSE

Reply 6

the bear

20

Original post by TenOfThem

SD is not in the standard GCSE

this website includes it in GCSE:

http://www.mathsrevision.net/gcse-maths-revision/statistics-handling-data/standard-deviation

:hmmmm2:

Reply 7

Galileo Galilei

14

Standard deviation is the square root of Variance.

Reply 8

StayCoolGuys

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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Reply 9

MathsMeister

OP

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

Reply 10

TenOfThem

Original post by MathsMeister

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

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"

Reply 11

Original post by TenOfThem

SD is not in the standard GCSE

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?

Reply 12

Original post by MathsMeister

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

You can - it's called the Mean Absolute Deviation (you might want to look this up!).

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.

Reply 13

BabyMaths

Original post by 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"

Based on my experiments this morning, computing mean absolute deviations and standard deviations for very large data sets, I don't think computation time is a reason to reject MAD.

(edited 9 years ago)

Reply 14

the bear

20

Original post by 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?

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* "

(edited 9 years ago)

Reply 15

Original post by 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* "

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.

Reply 16

BabyMaths

Original post by 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.

One day? See question 3 here.

Reply 17

TenOfThem

Original post by 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?

Really and the 2015 syllabus has even less statistics/probability

Reply 18

MathsMeister

OP

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.

Reply 19