I have an experiment that relies on measuring temperature as a function of a given condition. I change the condition, allow the temperature to stabilize as much as possible, then take 3 measurements in a row, which are all slightly different, as the values tend to oscillate.

For example, I might have a set of readings that looks like this:

X Temperature

10.1 80.3

10.8 82.1

10.3 78.9

20.4 100.2

20.0 101.1

20.2 101.0

30.1 139.1

30.0 140.2

30.0 138.2

Which I will combine to look like this:

uniqueX Xmean Xstd Tmean Tstd

_______ ______ ________ ______ _______

10 10.2 0.1 80.433 1.6042

20 20.2 0.2 100.77 0.49329

30 30.033 0.057735 139.17 1.0017

% Matlab code for computation

xNom = round(X);

[uniqueX,~,subs] = unique(xNom);

Tmean = accumarray(subs, T, [], @mean);

Tstd = accumarray(subs, T, [], @std);

Xmean = accumarray(subs, X, [], @mean);

Xstd = accumarray(subs, X, [], @std);

tb = table(uniqueX, Xmean, Xstd, Tmean, Tstd);

I'm wondering: what is the best way to plot such data, i.e. when three data points like this are combined to represent one point, what is the best value to use for the error bars on a plot of T vs X, for example in this case?

For example, I might have a set of readings that looks like this:

X Temperature

10.1 80.3

10.8 82.1

10.3 78.9

20.4 100.2

20.0 101.1

20.2 101.0

30.1 139.1

30.0 140.2

30.0 138.2

Which I will combine to look like this:

uniqueX Xmean Xstd Tmean Tstd

_______ ______ ________ ______ _______

10 10.2 0.1 80.433 1.6042

20 20.2 0.2 100.77 0.49329

30 30.033 0.057735 139.17 1.0017

% Matlab code for computation

xNom = round(X);

[uniqueX,~,subs] = unique(xNom);

Tmean = accumarray(subs, T, [], @mean);

Tstd = accumarray(subs, T, [], @std);

Xmean = accumarray(subs, X, [], @mean);

Xstd = accumarray(subs, X, [], @std);

tb = table(uniqueX, Xmean, Xstd, Tmean, Tstd);

I'm wondering: what is the best way to plot such data, i.e. when three data points like this are combined to represent one point, what is the best value to use for the error bars on a plot of T vs X, for example in this case?