PRECISION and ACCURACY How 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 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, BONNIE (in meters): 0.905, 0.900, 0.905, CARLOS (in meters): 1.002, 1.001, 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, cm Adam A P

EXAMPLE (cont’d) BONNIE (in meters): 0.905, 0.900, 0.905, cm Adam A P Bonnie A P

EXAMPLE (cont’d) CARLOS (in meters): 1.002, 1.001, 1.003, cm Adam A P Bonnie A P Carlos A P

EXAMPLE (cont’d) DOMINIC (in meters): 1.005, 1.000, 1.005, 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 cm is not.

THE END © Lilian Wehner