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