Rounding of Final Value with Sig Figs

[Browntown]

Homework Statement

Rounding of Final Value with Sig Figs

Relevant Equations

None

In my lab report, I average the values of the index of refraction of a prism and I calculated the average uncertainty from the uncertainties in all those measurements. My questions is my final value is 1.585 +/- 0.006

I'm assuming my uncertainty should be rounded to 0.01 but does that mean my value should be rounded to 1.59 or 1.60?

 

[hutchphd]

The purpose of rounding is to not display meaningless digits. By the same token you want to be sure not to throw away anything meaningful.
To my mind, unless you know your numbers are imprecise for some other reason, your final values should be reported as you initially state them.

 

[Orodruin]

and I calculated the average uncertainty from the uncertainties in all those measurements.

This is not how the overall uncertainty should be computed.

What exactly are your measurements and errors?

 

[hutchphd]

My apologies for not catching that.
You typically need to do an RMS average which will commonly be dominated by the largest error. Important to understand how this works.

 

[Browntown]

Thank you for the advice, I looked up RMS and got a better final value.

 

[Orodruin]

My apologies for not catching that.
You typically need to do an RMS average which will commonly be dominated by the largest error. Important to understand how this works.

This is not the proper procedure. In the proper procedure the average of the measurements must be a weighted average that will be dominated by the measurement with the smallest error. That error will also typically dominate the overall error (which will also be smaller than all individual errors since you are adding information). This is why I asked OP to post his original underlying data.

One also has to be very mindful of any systematic errors as those do not get better when combining measurements.