Error Analysis
Monday, August 17th
Do Now
 Complete
the following calculation. Make sure
you use the correct amount of sig figs:

4.5675x174.5

Once you get your answer, put it into scientific
notation
Accuracy and Precision
Accuracy
Precision
• How close you are to the
• How close your
actual value
measurements are to
• Example: The density of
one another
water is 1 g/mL. You are
• Precision refers to the
accurate if your
reproducibility of the
experimental value is
close to 1 (0.99, 1.01)
measurement and
exactness of
description in a number
Accuracy vs. Precision
Accuracy= bulls eye (or average out to bulls eye)
Precision = darts are close together
Precision
 To
decide on precision, you need
several measurements (notice
multiple arrow holes), and you do
not need to know the true value
(none of the values are close to the
target but all the holes are close
together.)
 A sample
is known to weigh 3.182 g. Jane weighed
the sample five different times with the resulting
data. Which measurement was the most accurate?




3.200 g
3.180 g
3.152 g
3.189 g
Mark each set of numbers as having a high or low
accuracy and precision.
Object measured is 50 cm length
 52
 60
 48
 41
Mark each set of numbers as having a high or low
accuracy and precision.
Object measured is 15 cm2 area
 13.21
 13.25
 13.19
 13.22
Mark each set of numbers as having a high or low
accuracy and precision.
Object measured is 32 g mass
 40
 55
 32
 50
Mark each set of numbers as having a high or low
accuracy and precision.
Object measured is 0.31 g/cm3 density
 0.30
 0.32
 0.31
 0.31
Expressing Errors in Measurement
g Errors in Measurement:
Scientists
often
express and
theirerror
uncertainty
and error
oftenexpress
their
uncertainty
in measurement
by giving
in measurements by giving a percent error. The
error. The
percent
error
is defined
percent
error
is defined
as:as:
actual value • measured value
% error =
x 100
actual value
e following four questions. Pay attention to significant figures, and s
*NOTICE, this is not percent yield
!
actual value
• measured
value and error in measurement by
Scientists %
often
their
uncertainty
error express
=
x 100
actual value
a percent error. The percent error is defined as:
Expressing Errors in Measurement
Answer the following four questions. Pay attention to significant figures, and show
actual value • measured value
your work!
% error =
x 100
actual value
1. While doing a lab, a student found the density of a piece of pure aluminum to be 2.85
3
g/cm3. Answer
The accepted
value for the
density
of aluminum
is 2.70 g/cm
What was the
the following
four
questions.
Pay attention
to. significant
figures
student's percent error?
your work!
1. While doing a lab, a student found the density of a piece of pure alum
g/cm3. The accepted value for the density of aluminum is 2.70 g/cm3
student's percent error?
Science, Measurement, and Uncertainty: Accuracy and Precision
2. A student measured the specific heat of water to be 4.29 J/g · Co. The literature
value of the specific heat of water is 4.18 J/g · Co. What was the student’s
percent error?
3. A student took a calibrated 200.0 gram mass, weighed it on a laboratory balance, and
found it read 196.5 g. What was the student’s percent error?
Error Analysis in Chemistry
There
are two sources of error in
chemistry labs:
1.
2.
Systematic Errors (determinate)
Random Errors (indeterminate)
Systematic Errors
 Errors
due to identifiable causes
 Likely to give results that are consistently too high
or too low
 Sources of error can usually be identified
 Affects accuracy
 Examples


Equipment being consistently wrongly used by
experimenter
Wrongly calibrated machine
Random Errors
 Sources
or error cannot always be identified
 The random error is equivalent to the uncertainty
in measurement.
 Affects precision
 Due to the precision limitations of the
measurement device. Random errors usually result
from the experimenter's inability to take the same
measurement in exactly the same way to get
exact the same number
How to Minimize Error
 Random:
take more data. Random error
can be reduced by averaging over a
large number of observations.
 Systematic: Be sure your instruments are
properly calibrated. (These are harder to
detect)
Reporting Data
 The
mean: or average value. Defined as
the sum of all of the values, divided by
the number of measurements.
Find the Mean