# Basic Standard Deviation

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#1
Find the standard deviation

15.6, 17.3, 19.4, 16, 18.3, 17.5

fx = 104.1
fx^2 = 1816.15

(1815.15 / 6) - (104.1 / 6)^2 = 1.5025 >>>>> sq1.5025 = 1.23

isnt giving me 1.42

where am i going wrong?
0
6 years ago
#2
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#3
(Original post by BabyMaths)

sorry im confused
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6 years ago
#4
(Original post by cera ess six)
sorry im confused
I get 1.31 as my standard deviation? In your workings you put 1815.15 when it should be 1816.5. Regardless I don't get 1.42 either.
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#5
(Original post by Super199)
I get 1.31 as my standard deviation? In your workings you put 1815.15 when it should be 1816.5. Regardless I don't get 1.42 either.
the calculator gives 1.42 as well the answer sheet so i guess we both doing something wrong
0
6 years ago
#6
Standard deviation = square root of [(the square of the means) minus (the mean of the squares)].
0
6 years ago
#7
Your calculator and the answer uses Bessel's correction. Which is using (N-1) instead of N. If you change 6 (N) to 5 (N-1) you'll get 1.42
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6 years ago
#8
(Original post by MuzzyYT)
Your calculator and the answer uses Bessel's correction. Which is using (N-1) instead of N. If you change 6 (N) to 5 (N-1) you'll get 1.42
That just gives you a maths error
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6 years ago
#9
(Original post by Super199)
That just gives you a maths error

15.6, 17.3, 19.4, 16, 18.3, 17.5

fx = 104.1 , mean = 17.35
fx^2 = 1816.15

Altered to correction.

Formula SQRT( (Fx^2/n) - (mean)^2)
SQRT ( 1816.5/6 - (17.35^2) = SQRT(1.669) = 1.29

Bessel's Correction. If it's an old question, maybe this is why this is used, otherwise it may be the context. I can only remember the correction for the alternate formula of SD, being the

SQRT( Sigma(X-mean)^2) / n)
SQRT(10.015/6) = SQRT(1.669) = 1.29

With Bessel's correction

SQRT(10.015/5) = SQRT(2.0164) = 1.42
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6 years ago
#10
Square root the variance
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6 years ago
#11
(Original post by cera ess six)
fx^2 = 1816.15

(1815.15 / 6) - (104.1 / 6)^2 = 1.5025 >>>>> sq1.5025 = 1.23

isnt giving me 1.42
The error above is part of the problem. The other problem is that you should apparently be using

standard deviation =

or .

This gives the unbiased estimate of the population standard deviation.
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#12
(Original post by BabyMaths)
The error above is part of the problem. The other problem is that you should apparently be using

standard deviation =

or .

This gives the unbiased estimate of the population standard deviation.

why do you have to do the (n-1)
0
6 years ago
#13
(Original post by cera ess six)
why do you have to do the (n-1)
It provides an unbiased estimate.
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6 years ago
#14
(Original post by cera ess six)
why do you have to do the (n-1)
This may not mean much at the moment but it does answer your question.
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6 years ago
#15
(Original post by MuzzyYT)
15.6, 17.3, 19.4, 16, 18.3, 17.5

fx = 104.1 , mean = 17.35
fx^2 = 1816.15

Altered to correction.

Formula SQRT( (Fx^2/n) - (mean)^2)
SQRT ( 1816.5/6 - (17.35^2) = SQRT(1.669) = 1.29

Bessel's Correction. If it's an old question, maybe this is why this is used, otherwise it may be the context. I can only remember the correction for the alternate formula of SD, being the

SQRT( Sigma(X-mean)^2) / n)
SQRT(10.015/6) = SQRT(1.669) = 1.29

With Bessel's correction

SQRT(10.015/5) = SQRT(2.0164) = 1.42
Ah I see... So when do we use Bessel's correction? We were never actually taught this so it's a new thing. But thanks
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6 years ago
#16
(Original post by Super199)
Ah I see... So when do we use Bessel's correction? We were never actually taught this so it's a new thing. But thanks
It was never even mentioned last year when I did stats in AS maths. The only reason I know about it is because we were taught SD in biology too, and there was a little fued as our Teacher and teacher's calculator used N-1, but this calculator was so old you had to practically shovel coal into it to make it work.

We were told it's usually used to remove bias and provide a better value from a sample which is not a totality.
For example if you were to measure the height of a sample of 20 giraffes, you'd probably use Bessel's Correction(N-1), but if you were to measure the height of every giraffe in existence, then it would be N.
1
6 years ago
#17
(Original post by Super199)
Ah I see... So when do we use Bessel's correction? We were never actually taught this so it's a new thing. But thanks
The only time you need to use it is if you have taken a sample of data from a population and you want to estimate the variance of the population from the sample data.

Unfortunately some statistics courses seems to include it as a "standard" alternative to the variance which is obtained by dividing by n, and this leads to a lot of confusion!
1
#18
(Original post by BabyMaths)
This may not mean much at the moment but it does answer your question.

(Original post by MuzzyYT)
15.6, 17.3, 19.4, 16, 18.3, 17.5

fx = 104.1 , mean = 17.35
fx^2 = 1816.15

Altered to correction.

Formula SQRT( (Fx^2/n) - (mean)^2)
SQRT ( 1816.5/6 - (17.35^2) = SQRT(1.669) = 1.29

Bessel's Correction. If it's an old question, maybe this is why this is used, otherwise it may be the context. I can only remember the correction for the alternate formula of SD, being the

SQRT( Sigma(X-mean)^2) / n)
SQRT(10.015/6) = SQRT(1.669) = 1.29

With Bessel's correction

SQRT(10.015/5) = SQRT(2.0164) = 1.42

do you have to do the whole (n-1) all the time when working out SD im sure in the past ive done it with just using N and got the correct answer
0
6 years ago
#19
(Original post by cera ess six)
do you have to do the whole (n-1) all the time when working out SD im sure in the past ive done it with just using N and got the correct answer
See my previous answer! The n-1 version is only for estimating population variance from a sample of data - ordinarily n should be used.
(This does not stop books, authors who should know better, and even exam questions, from getting it wrong )
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6 years ago
#20
(Original post by MuzzyYT)
It was never even mentioned last year when I did stats in AS maths. The only reason I know about it is because we were taught SD in biology too, and there was a little fued as our Teacher and teacher's calculator used N-1, but this calculator was so old you had to practically shovel coal into it to make it work.

We were told it's usually used to remove bias and provide a better value from a sample which is not a totality.
For example if you were to measure the height of a sample of 20 giraffes, you'd probably use Bessel's Correction(N-1), but if you were to measure the height of every giraffe in existence, then it would be N.
I take it that most question in AS maths tend to be on just n and not n-1?
0
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