# Thread: Sample standard deviation with multiple measuring devices

1. ## Sample standard deviation with multiple measuring devices

I have a problem where let's say I use ten thermocouples to measure the same air temperature. Each one gives 30 readings. What is the sample standard deviation?

Initially I would think to take all 300 data points and calculate the sample standard deviation from that, but that discounts systematic error. Unfortunately, using a spatial standard deviation discount the random error. What is the right thing to do? I know ultimately in the uncertainty I will take into account all the error sources, but I'm hung up on what the sample standard deviation should be.

Thanks.

2. ## Re: Sample standard deviation with multiple measuring devices

let me get this right

you have a spatial field of thermocouples set up

the temperature across that spatial field can vary a bit

each thermocouple can have some systematic and random error to it

you want to combine the measurements from all these thermocouples in a meaningful way so as to....

what?

get the average temperature across the field?

3. ## Re: Sample standard deviation with multiple measuring devices

Originally Posted by romsek
let me get this right

you have a spatial field of thermocouples set up

the temperature across that spatial field can vary a bit

each thermocouple can have some systematic and random error to it

you want to combine the measurements from all these thermocouples in a meaningful way so as to....

what?

get the average temperature across the field?
Yes, I'm taking the average of the measurements to get a single temperature for the test. I have done that, but I must find the sample standard deviation as well. That is what I am having issues with.

4. ## Re: Sample standard deviation with multiple measuring devices

Originally Posted by Haff174
Yes, I'm taking the average of the measurements to get a single temperature for the test. I have done that, but I must find the sample standard deviation as well. That is what I am having issues with.
last question.

These thermocouples. Do you have data on their systematic bias ahead of time or do you have to estimate this from the data you are taking?

5. ## Re: Sample standard deviation with multiple measuring devices

Hi Haff174.

Can you show us some assumptions for the distribution of the sample?

6. ## Re: Sample standard deviation with multiple measuring devices

Originally Posted by romsek
last question.

These thermocouples. Do you have data on their systematic bias ahead of time or do you have to estimate this from the data you are taking?
Just so I don't confuse my tenses, let's assume I have already performed the test and have acquired all of the data.

I do have the accuracy of the instruments (b1) and have calculated the spatial contribution part of the systematic error (b2). Let's say those are the two systematic errors. So total the systematic error (b) is (b1^2+b2^2 )^0.5.

The random portion of the uncertainty I have calculated by:

sigma(average TC) = sqrt(sigma(TC1)^2 + sigma(TC2)^2 +... sigma(TC10)^2)/10

where sigma(TC#) represents the random error from each thermocouple measurement (sample standard deviation of each thermocouple). The total uncertainty should just be the RSS of the systematic and random errors:

(sigma(average TC)^2+b^2)^0.5

So you all can check to see if I understand that much. My problem here is I need not only the total uncertainty, but also the sample standard deviation of the average temperature... I think the math here tells me that the sample standard deviation is just the random error (sigma(average TC)) portion of the uncertainty, but I am not sure.

Originally Posted by chiro
Hi Haff174.

Can you show us some assumptions for the distribution of the sample?
I think it is safe to assume a normal distribution since these thermocouples are measuring the same thing. Is that sufficient?