[tou]

Hi

When I have many results, for example:

Temperature ___ Change / 3 trials
20_____________4_____3____2
30_____________ 5____2____1

I know that apparatus that measures the change has an uncertainty of 0.5, so I use it in the raw data.

When I calculate the average:

20______3
30______2.67

How do I know my uncertainty now? I read through a few websites but I am still not sure. Is it the average standard deviation? Thus I calculate the standard deviation for each temperature of all trials and the take the average of both temperatures?

Further, should you always have the same decimal place? So, its 20.00, 30.00, 3.00 and 2.67?

What if the apparatus has an uncertainty of 0.2 but your result is 3.42. Should you write 0.20?

Thanks!

[enahs]

What if the apparatus has an uncertainty of 0.2 but your result is 3.42. Should you write 0.20?

If you device has uncertainty to 1 decimal place, how can you measure to two decimal places?

Though, I am not really sure what your raw data and what is going on. It is very confusing how you have it written??

For the propagation of error in calculations:
http://www.chem.usu.edu/~sbialkow/Classes/3600/Overheads/Propagation/Prop.html

[tou]

Thats what I found about the pH meter:
Resolution: 0 .01 pH
Accuracy: ±0.2pH

The raw data in the first post was just an example, its random. It can be anything.

I just want to know what I have to do with the uncertainty when I calculate the average of data. So, I have 3 trials; I measure the pH: 6.53, 6.57, 6.52. Thus the average pH is 6.54. I know that the uncertainty of the raw data is 0.2 because thats the accuracy of the pH meter. What is now the uncertainty of the average 6.54?

Then I also wanted to know what happens with the uncertainty of the average if I have not just 3 trials but also, lets say, 3 different temperatures. Thus I measure the pH at different temperatures (for example).

"Table":
Temperature____pH
20...6.53....6.57....6.52....
30...
40..

When I calculate the average of all 3 trials for each temperature, doesn't the uncertainty vary for each average? Thus, for 20°C the average is 6.54, for 30°C 6.20 and for 40°C 6.00. Now I calculate the uncertainty for the first average 6.54 - doesn't it differ from that of 6.20?

Furthermore, I was actually also wondering why the uncertainty is 0.2 and the pH meter measures 2 decimal places. Thats why I asked if the I shouldn't write 0.20?

I hope its clearer now...

[Arkcon]

Let me work with just this part of your question ...

Furthermore, I was actually also wondering why the uncertainty is 0.2 and the pH meter measures 2 decimal places. Thats why I asked if the I shouldn't write 0.20?

The instrument is accurate and precise to +/- 0.2 pH unit.  If you measure the same solution repeatedly, you can expect the numbers to be within 0.2 pH unit of each other, and you can check, if you feel like it.  Why does it report answers to 0.xx and not just round off for you?  That one's easy.  So you'll think it's a better meter at first glance and buy it.  That's it.  Pure marketing.

I'm not kidding about this.  Often, at companies I've worked at, someone from maintenance will come up with their little hand held pH meter, and try to find out why it's output is not consistent.  Those little P.O.S. meters report accuracy the same as yours, +/- 0.2, but they still use them to the 0.01.  Sometimes they listen to my explanation when the come to compare it with my lab pH meter, and sometimes they don't.

[tou]

That's kind of funny  ...

But how do I calculate the uncertainty for the average? So, I know its 0.2 for the raw data, what happens to this uncertainty when I calculate the average of the raw data? Is there any special calculation I have to do, or does it just remain 0.2?

[enahs]

Go to the website I linked previously..