Standard Deviation S1 help!!

Sherlock.and.John

The questions is worded as follows:

'The mean and standard deviation of the heights of 12 boys in a class are 148.8cm and 5.4cm respectively. A boy of height 153.4cm joins the class. Find the mean and standard deviations of the heights of the 13 boys.’

I managed to find out the new mean and it is 149.1538. For the second part I know you need to use the formula of variance: 1⁄nΣ( x−(the mean of x))^2 x=the total of all of the heights added together. But whenever I use this formula it never seems to work :confused:

so I am now consulting the amazing people on TSR to see if they can help :smile:

Thanks in advance.

(edited 12 years ago)

Reply 1

ian.slater

12

Original post by Sherlock.and.John

The questions is worded as follows:

'The mean and standard deviation of the heights of 12 boys in a class are 148.8cm and 5.4cm respectively. A boy of height 153.4cm joins the class. Find the mean and standard deviations of the heights of the 13 boys.’

I managed to find out the new mean and it is 149.1538. For the second part I know you need to use the formula of variance: 1⁄nΣ(𝓍−(the mean of x)) 𝓍=the total of all of the heights added together. But whenever I use this formula it never seems to work :confused:

so I am now consulting the amazing people on TSR to see if they can help :smile:

Thanks in advance.

You might have met the formulae in the form of sum-of-x and sum-of-x^2 which should make this one easy.

Reply 2

Sherlock.and.John

OP

8

Original post by ian.slater

You might have met the formulae in the form of sum-of-x and sum-of-x^2 which should make this one easy.

No I haven’t :/ But it’s part of an exercise based around that formula.

OP

bump

Original post by Sherlock.and.John

No I haven’t :/ But it’s part of an exercise based around that formula.

You will have met:

mean of n items = (sum-of-x)/n

and there is a formula for variance that looks like:

variance of n items = ((sum-of-x^2)/n) - mean^2

and then s.d. = sqrt(variance)

Sometime the n in the variance formula is replaced by (n-1). The difference isn't explained at A level - you just need to make sure you're following the rule in your textbook.

Reply 5

Sherlock.and.John

OP

8

Original post by ian.slater

You will have met:

mean of n items = (sum-of-x)/n

and there is a formula for variance that looks like:

variance of n items = ((sum-of-x^2)/n) - mean^2

and then s.d. = sqrt(variance)

Sometime the n in the variance formula is replaced by (n-1). The difference isn't explained at A level - you just need to make sure you're following the rule in your textbook.

ahh ok thank you! i will try that now

Reply 6

Luminescent

The S.D. is 5.4
Therefore the variance is 5.4^2
Variance is the sum of the squares of the data divided by the amount of data minus the square of the mean.
So add the square of the old mean, multiply by 12, add this new height (153.4cm) squared to the sum, divide this new sum by 13 and subtract the square of your new mean. Square root this for the new S.D.
I've used the alternative variance formula for this question as it's easier, but it's equivalent to the first one. They should both be in your text book with a proof of the equivalence. Sorry that this was a bit wordy, but I haven't got round to learning LaTeX yet and text-formulae are awful.