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Error Analysis Lab Report
Physics 11411, Lab 1
August 27, 2010
Patrick Mooney
Lab Partners: Kyle Broflowski
Purpose:
We are asked to determine how many drops of water a bucket of water can hold. This can be
useful if one wanted to know how much bacteria is in a bucket of water if given the number of
bacteria per droplet of water.
Background:
The measurement of the mass of the water can normally be used by simply weighing the water
on a scale and measuring how much that weighs minus whatever the container’s mass is.
However, this method doesn’t affirm that the scale is statistically precise, and so, one must weigh
such a mass of water multiple times and find the mean of those numbers. To find the mean, one
must use the formula
x
=
=
1Ni 1Nxi
, where N is the number of trials done. The mean is only an
estimate, however, and there will be a statistical uncertainty or error associated with it. To find
the error, one must first find the standard of deviation, which can be found with the formula
sx
=
((
 ) =
(
1N 1 i 1N

x
)
xi 2
), where N is the number of trials and
x
is the mean. The error on the
mean is then simply
σx
=
sxN
. This gives us the mean and the error on that mean for an
individual measurement. When combining measurements using mathematical operations, one
has to find the uncertainty on the new value. For instance, if two individual measurements A and
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 Spring '10
 Smith
 Physics

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