# Correctly Scaling the Standard Deviation for Scaled Measurements

• I
• camilleon
In summary: I copied and pasted this text from another forum and forgot to check the formatting for the equations here. The factor should have been $$\left(\frac 3 {nu}\right)$$ but very close. I think the increase in the error bars is probably due to error in nu. Thank you!
camilleon
TL;DR Summary
I have a standard for each individual value in a set of data. After scaling this data, the standard deviations must be scaled as well.
We're working on a project that plots flux density of a light curve with respect to time. To do this, we had to scale data from different wavelengths so we had just the one variable for the flux. Essentially we took each value for flux density and multiplied it by three over the frequency raised -1/2 power..
Sscaled=S⋅(3nu)−12Sscaled=S⋅(3nu)−12Where S is our flux denisty, nu is the frequency, and S_scaled in the scaled flux density (what we're going to plot)

QUESTION: We know the standard deviation for each measurement of flux density and we also want to scale it accordingly. This is where I'm having trouble. I'm not familiar with how to properly scale standard deviation in this case. We're essentially multiplying each value by a different number. Would I simply multiply each value for standard deviation by the same factor? That would be,
Errscaled=Serr⋅(3nu)−12Errscaled=Serr⋅(3nu)−12Where S_err is the standard deviation for each measurement and Err_scaled is the scaled standard deviation

We tried this and it gave us pretty large error bars. Since I'm not sure this is the right formula, I wanted to sure this is the correct way to scale the standard deviation.

Hello camilleon, !

Can you typeset your equations ? It is impossible for me to deciper something like
Sscaled=S⋅(3nu)−12Sscaled=S⋅(3nu)−12

If I try to make sense I get something that may or may not be correct:
I type $$S_{scaled}=\frac {S}{\sqrt{3\nu}}\quad ?$$ and get
$$S_{scaled}=\frac {S}{\sqrt{3\nu}}\quad ?$$

If the error in ##\nu## is negligible, then the error in ##A## times ##S## is the error in ##A## times the error in ##S##

which may or may not be the expression you intended to post that came out as Errscaled=Serr⋅(3nu)−12Errscaled=Serr⋅(3nu)−12
(guidelines point 7)

camilleon said:
We tried this and it gave us pretty large error bars.
Were the error bars different before ?

Standard deviations scale by the same factor as the individual measurements.

camilleon
BvU said:
Hello camilleon, !

Can you typeset your equations ? It is impossible for me to deciper something like

If I try to make sense I get something that may or may not be correct:
I type $$S_{scaled}=\frac {S}{\sqrt{3\nu}}\quad ?$$ and get
$$S_{scaled}=\frac {S}{\sqrt{3\nu}}\quad ?$$

If the error in ##\nu## is negligible, then the error in ##A## times ##S## is the error in ##A## times the error in ##S##

which may or may not be the expression you intended to post that came out as Errscaled=Serr⋅(3nu)−12Errscaled=Serr⋅(3nu)−12

Sorry, I copied and pasted this text from another forum and forgot to check the formatting for the equations here. The factor should have been $$\left(\frac 3 {nu}\right)$$ but very close.
I think the increase in the error bars is probably due to error in nu. Thank you!

(guidelines point 7)

So the
camilleon said:
raised -1/2 power..
Has disappeared now ? I figured it was to be deciphered from the "S⋅(3nu)−12 "

Are you also going to make plots of things derived from ##S## with frequency on the x-axis ?

Re:
copied and pasted this text from another forum

## 1. What is the purpose of scaling the standard deviation for measurements?

The purpose of scaling the standard deviation for measurements is to adjust the standard deviation to account for any changes in the units or scale of the measurements. This allows for a more accurate representation of the variability in the data.

## 2. How is the standard deviation scaled for measurements?

The standard deviation is scaled by dividing it by the scaling factor, which is calculated by dividing the new standard deviation by the original standard deviation. This ensures that the scaled standard deviation has the same relative size as the original standard deviation.

## 3. Can the standard deviation be scaled for any type of measurement?

Yes, the standard deviation can be scaled for any type of measurement as long as the scaling factor is calculated correctly. This applies to both continuous and discrete measurements.

## 4. Does scaling the standard deviation change the shape of the data distribution?

No, scaling the standard deviation does not change the shape of the data distribution. It only adjusts the scale of the standard deviation to match the new units or scale of the measurements.

## 5. What is the difference between scaling the standard deviation and converting the units of measurement?

Scaling the standard deviation adjusts the value of the standard deviation to match the new units or scale of the measurements, while converting the units of measurement changes the actual values of the measurements themselves. Both methods can be used to account for changes in units or scale, but they serve different purposes.

• Set Theory, Logic, Probability, Statistics
Replies
4
Views
1K
• Set Theory, Logic, Probability, Statistics
Replies
15
Views
2K
• Set Theory, Logic, Probability, Statistics
Replies
21
Views
2K
• Set Theory, Logic, Probability, Statistics
Replies
6
Views
1K
• Set Theory, Logic, Probability, Statistics
Replies
7
Views
2K
• Set Theory, Logic, Probability, Statistics
Replies
1
Views
1K
• Introductory Physics Homework Help
Replies
3
Views
2K
• Set Theory, Logic, Probability, Statistics
Replies
19
Views
1K
• Set Theory, Logic, Probability, Statistics
Replies
1
Views
1K
• Chemistry
Replies
3
Views
789