Standard Deviation: What Does it Measure & Agreeing with G?

[mewmew]

Well in physics lab we just did a lab where we calculated the acceleration do to gravity,this didn't include the air resistance, so the ligther stuff shouldn't be perfect. We took video of stuff falling and then put the data from that into mathematica and fitted a quadratic equation to it and then calculated g from that equation. Now, of course the lightest ball had the worst acceleration and that data all came out correct. But my question is, we have to find the standard deviation but I have ran into a bit of a problem. First off, I don't really know what standard deviation is, in simple terms I think it is just a measure of the average deviation each point holds from the theoretical point it should be at, but I am not really sure what it actually measures and what kind of units? Also, my standard deviations didn't line up with the values I got for g, for example, I got a lower standard deviation for one the lighter object, even though gravity came out the farthest from 9.8 for that one. Is it possible for standard deviation to not agree with my calculated g? Thanks a lot for any help

 

[Integral]

In ideal normally distributed data, ~60% of your data will be within 1 standard deviation of the mean. So the standard deviation is a measure of the spread of your data. The smaller the standard deviation the better your data is. The Std Dev should be in the same units as your measured value.

 

[ZapperZ]

Well in physics lab we just did a lab where we calculated the acceleration do to gravity,this didn't include the air resistance, so the ligther stuff shouldn't be perfect. We took video of stuff falling and then put the data from that into mathematica and fitted a quadratic equation to it and then calculated g from that equation. Now, of course the lightest ball had the worst acceleration and that data all came out correct. But my question is, we have to find the standard deviation but I have ran into a bit of a problem. First off, I don't really know what standard deviation is, in simple terms I think it is just a measure of the average deviation each point holds from the theoretical point it should be at, but I am not really sure what it actually measures and what kind of units? Also, my standard deviations didn't line up with the values I got for g, for example, I got a lower standard deviation for one the lighter object, even though gravity came out the farthest from 9.8 for that one. Is it possible for standard deviation to not agree with my calculated g? Thanks a lot for any help

Your standard deviation is NOT supposed to "agree" with the value of "g". The std. dev. doesn't know about g. It only tells you by how much your data is spread out from the mean value over repeated measurements. The fact that the lighter objects give you data with the wrong g but a smaller std. dev. is perfectly acceptable. It just means that your lighter objects have data that hover around a smaller range of values than the larger ones.

In most cases, what you want to look for is that the correct value of "g" falls within 1 std. dev. from the mean value that you found, or at least, find out how far from the mean value. Normally, if your mean value is more than 1 std. dev. away from the accepted value, then there is a systematic error in the measurement which you should account for in your lab report.

Zz.

 

[mewmew]

Thank you both very much, that helps a lot!