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Accuracy and Precision
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Accuracy and Precision• Since all measurements contain an estimated
digit, all measurements contain some uncertainty (error).
• Scientists try to limit the uncertainty (error) as much as possible but they cannot eliminate it.
• There are three main reasons for uncertainty in measurements:
i. instrumental error
ii. observer error
iii. procedural error
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Accuracy and Precisioni. Instrumental Error:
All measuring instruments have error. The more sensitive and precise the instrument is, the lower the amount of error will be.
A more sensitive instrument will give more significant figures than a less sensitive one.
A more precise instrument will give the same reading more often than a less precise one.
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Accuracy and Precisionii. Observer Error:
An instrument is only as good as the person using it! Persons who have more experience and who take more precautions will generally record measurements with less error.
iii. Procedural Error:
Measurements can have error due to faulty experimental procedure.
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Accuracy and Precision• In an experiment, it is important to be able to
state the level of confidence of one’s data.
• In this course, you will analyze the accuracy and the precision of data.
• Accuracy measures how close a measured value is to the accepted value
• Precision measures how close together several measured trials are to one another.
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Accuracy and Precision• In this course you will use percent error to
measure accuracy.
%Error = Measured Value – Accepted Value 100
Accepted Value
• %Error can be positive or negative!
• %Error < than |5%| = high accuracy.
• |5%| ≤ %Error ≤ |10%| = moderate accuracy.
• %Error > |10%| = low accuracy.
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Accuracy and Precision• In this course, precision will be measured by the
“eyeball test”.
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Accuracy and Precision• In this course, precision will be measured by the
“eyeball test”.
high precision
high precision
low precision
moderate precision
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Accuracy and PrecisionEx. (1) If a class gathered the following density
data for substance X, then calculate the accuracy of the data if the accepted value were 3.68 g/mL?
3.60 g/mL, 3.58 g/mL, 3.69 g/mL, 3.63 g/mL,
3.65 g/mL, 3.56 g/mL, and 3.70 g/mL
Average = = 3.63 g/mL
The precision appears high
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Accuracy and Precision%E = M – A 100
A
%E = 3.63 g/mL – 3.68 g/mL 100 3.68 g/mL
%E = - 0.05 g/mL 100 3.68 g/mL
%E = - 1 %
one sig. fig.
high accuracy and high precision
-0.05 g/mL
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Accuracy and PrecisionEx. (2) Determine the accuracy for the following
specific heat data (to two significant figures,
the accepted value = 0.095 cal/goC).
Trial # 1 2 3 4 5 6 7 8
cal/goC 0.110 0.080 0.098 0.087 0.092 0.103 0.090 0.100
Average = = 0.095 cal/goC
The precision appears low
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Accuracy and Precision%E = M – A 100
A
%E = 0.095 cal/goC – 0.095 cal/goC 100 0.095 cal/goC
%E = 0.000 cal/goC 100 0.095 cal/goC
%E = 0 % high accuracy but low precision
0.000 cal/goC
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Accuracy and PrecisionEx. (3) If a student gathered the following heat of
fusion of ice data (90.4 cal/g, 83.9 cal/g, 93.2 cal/g, 78.4 cal/g, and 96.8 cal/g),
then what is the accuracy of the student’s data? (to three significant figures, Hf of ice is
accepted to be 80.0 cal/g)
Average = = 88.5 cal/g
The precision appears low
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Accuracy and Precision%E = M – A 100
A
%E = 88.5 cal/g – 80.0 cal/g 100 80.0 cal/g
%E = 8.5 cal/g 100 80.0 cal/g
%E = 11 %
two sig. figs.
low accuracy and low precision
8.5 cal/g
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Accuracy and PrecisionEx. (4) Calculate the accuracy of this melting point
of phosphorus data (accepted value =
44.1oC).
Trial # 1 2 3 4 5 6 7 8
oC 48.3 49.1 49.5 48.4 49.2 48.0 48.8 49.7
Average = = 48.9oC
The precision appears high
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Accuracy and Precision%E = M – A 100
A
%E = 48.9oC – 44.1oC 100 44.1oC
%E = 4.8oC 100 44.1oC
%E = 11 %
two sig. figs.
low accuracy but high precision
4.8oC