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Accuracy and Precision
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
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.
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.
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.
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.
Accuracy and Precision• In this course, precision will be measured by the
“eyeball test”.
Accuracy and Precision• In this course, precision will be measured by the
“eyeball test”.
high precision
high precision
low precision
moderate precision
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
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
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
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
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
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
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
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