# Homework Help: I need help in deciding what my error bars should be

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1. Dec 30, 2015

### jb95

• Member advised to use the homework template for posts in the homework sections of PF.
So, we did an experiment to find the dissolved oxygen concentration in % over time in a stirred tank reactor at 2 different flow rates and at 3 different agitator speeds. We did not do any repeat measurements, it was just one reading per condition. Now I am confused what sort of error bars I could include on my graph. I have fitted a line of best fit for the data. Error bars are usually standard errors of the mean but no repeats were done and hence I have no mean value to base it on. Should the error bars in this case be uncertainties in the variable arising from measuring instruments. Are there curve fitting error bars I could use here? If yes, what could they be?
Btw I am plotting 3 graphs in total. In the first graph, I am plotting three sets of data, each set representing the particular agitator speed, of DO% against time. The first one is for flow rate of 5L/min. The second graph is for flow rate of 10 L/min, and again there are 3 sets of data of DO against time. The 3rd graph is of Mass transfer coefficient*Area (Kla) vs agitator speed. There would be 2 lines on the same graph because each line corresponds to a flow rate condition. I have fitted a best fit line on the first two graphs to calculate the gradient and hence Kla. I think I will put a trendline for Kla vs speed graph too.

2. Dec 30, 2015

### Dr. Courtney

In most cases, an experimenter needs repeated measurements under the same conditions to have error bars, and the standard error of the mean is used to estimate the uncertainties. https://en.wikipedia.org/wiki/Standard_error

Occasionally, one does include instrumental uncertainties to the standard error of the mean by adding the uncertainties in quadrature, but using only the instrumental uncertainties is equivalent to assuming the standard error of the mean is zero, which isn't really right either.

I think the bottom line is you need to repeat measurements under the same conditions to have reasonable estimates on the uncertainties.

3. Jan 2, 2016

### jb95

Thank you Dr. Courtney. I just had one more thing to check with you for this lab report. If a quantity x is some function of 1/y^3 (y is being measured), the percentage uncertainty in y is 0.7%, then the would the percentage uncertainty propagated in x be 3*0.7?

4. Jan 2, 2016

### Dr. Courtney

There are many times when uncertainties propagate like this.