PRECISION and ACCURACYHow low can you go?

CONTEXT

• There are two contexts precision and accuracy apply to: sets of data, and measuring instruments.

• In a set of data, those measures give an idea of the spread and “ballpark” of the answer (final measurement).

• In an instrument, those measures give you information about the best measurement possible with it.

PRECISION and ACCURACY

I. SETS of DATA

ACCURACY• In archery or rifle shooting, it is a measure of

how well shots are around the bull’s eye.ACCURATE NOT ACCURATE

NOTE: WE DON’T SAY “INACCURATE”, BUT “NOT ACCURATE"

PRECISION• In archery or rifle shooting, it is a measure of

how close shots are to each other. PRECISE NOT PRECISE

NOTE: WE DON’T SAY “IMPRECISE”, BUT “NOT PRECISE”

ACCURACY• In data, it is a measurement of how close the

set of data is to the actual value.

ACTUAL VALUE

AVERAGE (NOT ACCURATE)

AVERAGE (ACCURATE)

ACCURACY• In data, it has to do with the location of the

average, relative to the actual measurement:

ACTUAL VALUE

POOR ACCURACY

GOOD ACCURACY

PRECISION• In data, it is a measure of how close the data

points are to each other, regardless of the actual value.

ACTUAL VALUE

AVERAGE (PRECISE)

AVERAGE (NOT PRECISE)

PRECISION• In data, it is given by a measure of how the

data points are spread around the average.

ACTUAL VALUE

GOOD PRECISION

POOR PRECISION

ACCURACY• To calculate the accuracy of a set of points, find

the average of them, and compare with the actual measurement.

Ex: the average of 1.001m, 1.002m, 1.003m and 1.002m is 1.002m.

• If the actual value is 1.000m, the data is accurate. If the actual value is 0.900 m, the data is NOT accurate.

PRECISION• To check the data for precision, find out the

difference between the largest and smallest measurements in the set. This is the “spread” of the data about the average.

Ex: for the previous numbers, the spread is 0.002m around the average of 1.002m.• If the spread is small, the data is precise. If it is

large, the data is NOT precise.

EXAMPLE

• Four students (A, B, C and D) measure 4 times each the length of a desk (actual length: 90 cm). Their results are below. Check each set for precision and accuracy.

• ADAM (in meters): 0.902, 0.901, 0.903, 0.903• BONNIE (in meters): 0.905, 0.900, 0.905, 0.910• CARLOS (in meters): 1.002, 1.001, 1.003, 1.003• DOMINIC (in meters): 1.005, 1.000, 1.005, 1.010

EXAMPLE (cont’d)

• ADAM (in meters): 0.902, 0.901, 0.903, 0.903

90 cm

Adam A P

EXAMPLE (cont’d)

• BONNIE (in meters): 0.905, 0.900, 0.905, 0.910

90 cm

Adam A P

Bonnie A P

EXAMPLE (cont’d)

• CARLOS (in meters): 1.002, 1.001, 1.003, 1.003

90 cm

Adam A P

Bonnie A P Carlos A P

EXAMPLE (cont’d)

• DOMINIC (in meters): 1.005, 1.000, 1.005, 1.010

90 cm

Adam A P

Bonnie A P Carlos A P

Dominic A P

PRECISION and ACCURACY

II. MEASURING INSTRUMENTS

ACCURACY• In a measuring instrument, it is how much the

smallest interval in a measuring instrument is worth.

ACCURACY• In a measuring instrument, it is how much the

smallest interval in a measuring instrument is worth.

• It is the “gap” between two marked lines on it.

ACCURACY

PRECISION• In a measuring instrument, it is half of the

accuracy.

PRECISION• In a measuring instrument, it is half of the

accuracy.

• It is the error in a single measurement (also, the error in each individual measurement).

PRECISION• In a measuring instrument, it is half of the

accuracy.

• It is the error in a single measurement (also, the error in each individual measurement).

• ONE CANNOT MEASURE BEYOND THE PRECISION OF THE INSTRUMENT!

For example…

• … if the accuracy of a ruler is 2 mm, then the precision is 1 mm. This means that measurements made with the ruler extend to the millimeter place, but not beyond that:

So…10.1 cm, 10.5 cm and 10.8 cm are OK,

but 10.05 cm is not.

THE END

© Lilian Wehner