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 Precision i.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 Precision ii.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 Precision Ex. (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 appearshigh

Accuracy and Precision %E = M – A  100 A %E = 3.63 g/mL – 3.68 g/mL  g/mL %E = g/mL  g/mL %E = - 1 % one sig. fig. high accuracy and high precision g/mL

Accuracy and Precision Ex. (2) Determine the accuracy for the following specific heat data ( to two significant figures, the accepted value = cal/g o C ). Trial # cal/g o C Average == cal/g o C The precision appearslow

Accuracy and Precision %E = M – A  100 A %E = cal/g o C – cal/g o C  cal/g o C %E = cal/g o C  cal/g o C %E = 0 % high accuracy but low precision cal/g o C

Accuracy and Precision Ex. (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 appearslow

Accuracy and Precision %E = M – A  100 A %E = 88.5 cal/g – 80.0 cal/g  cal/g %E = 8.5 cal/g  cal/g %E = 11 % two sig. figs. low accuracy and low precision 8.5 cal/g

Accuracy and Precision Ex. (4) Calculate the accuracy of this melting point of phosphorus data ( accepted value = 44.1 o C ). Trial # oCoC Average == 48.9 o C The precision appearshigh

Accuracy and Precision %E = M – A  100 A %E = 48.9 o C – 44.1 o C  o C %E = 4.8 o C  o C %E = 11 % two sig. figs. low accuracy but high precision 4.8 o C