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I have 3 repitions of an experiment. The data consists of mass flow rates vs. time.

What I want to do is to calculate the mass vs. time, i.e. integrating my data.

I consider the resolution for each measurement to be exactly 3 minutes. To calculate the area I use the trapetzoid

rule, i.e. [itex](y(i)+y(i+1))/2*\Delta X= (y(i)+y(i+1))/2*3[/itex]

Now I want calculate the error. I know using the trapetzoid rule introduce errors, but since I

have no way of knowing how this affects my result I don't care about that particular error. Rather I want to know

the error between my 3 repititions.

My data look like this:

X # 1 # 2 # 3

0 y11 y21 y31

3 y12 y22 y32

6 y13 y23 y33

. . . .

. . . .

. . . .

n y1n y2n y3n

where y is mass flow rates and x is time.

This is my approach:

Calculate the mean mass flow rate, i.e

[itex]yavg(1)=(y11+y21+y31)/3[/itex]

[itex]yavg(2)=(y12+y22+y32)/3[/itex]

[itex]yavg(3)=(y13+y23+y33)/3[/itex]

...

[itex]yavg(n)=(y1n+y2n+y3n)/3[/itex]

and also the standard deviation

[itex]ystd(1)=std(y11,y21,y31)[/itex]

[itex]ystd(2)=std(y11,y21,y31)[/itex]

[itex]ystd(3)=std(y11,y21,y31)[/itex]

...

[itex]ystd(n)=std(y11,y21,y31)[/itex]

Then use the trapetzoid rule:

[itex]Area(1)=(yavg(1)+yavg(2))/2*3[/itex]

[itex]Area(2)=(yavg(2)+yavg(3))/2*3[/itex]

...

[itex]Area(n-1)=(yavg(n-1)+yavg(n))/2*3[/itex]

But how do I calculate the error? This I what I think:

[itex]Error(1)=sqrt((ystd(1)^2+ystd(2)^2)/2*3))[/itex]

[itex]Error(2)=sqrt((ystd(2)^2+ystd(3)^2)/2*3))[/itex]

or should it be like this:

[itex]Error(1)=sqrt(ystd(1)^2+ystd(2)^2)[/itex] ??

[itex]Area(1)+-Error(1)[/itex]

[itex]Area(2)+-Error(2)[/itex]

.. etc

And suppose I want to calculate the total mass, i.e Area(1)+Area(2)...+Area(n-1), then what will the error be?

Thanks

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# How do I calculate the error of my data?

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