Measurement and Uncertainty Key Points

Question 1

Error

Answer 1

the difference between the measured value and the true measurement. The amount of error is an expression of the accuracy or the measurement

Question 2

Uncertainty

Answer 2

quantification of the doubt about the measurement. Any error whose value is unknown is a source of uncertainty

Question 3

The uncertainty is an expression of the interval in which…

Answer 3

the true value of a measured value is likely to occur

Question 4

Uncertainty comes from what 3 things

Answer 4

• limitations of the techniques used to make the measurements
• the resolution of the measurement tool
• properties of the thing being measured

Question 5

what is a SINGLE POINT measurement

Answer 5

established zero point so the uncertainty is ½ of ± the smallest division of the measurement tool

Question 6

what is a TWO-POINT measurement

Answer 6

inability to guarantee the zero point so the uncertainty is ± the smallest division for each end of the measurement/measurement tool
- allows an estimate of the zero error (i.e., the error created) because of the inability to guarantee the 0 point

Question 7

uncertainty in REPEATED measurements (2 ways)

Answer 7

• the range divided by 2. If there is an outlier, then this approach will overestimate the uncertainty
• the calculation of the standard deviation or variance in the data

Question 8

uncertainty using DIGITAL tools

Answer 8

uncertainty is ± the last significant digit or the value specified by calibration of the tool or specified in the manual

Question 9

absolute uncertainty

Answer 9

values calculated using the appropriate approach (single, two, repeated, digital)

Question 10

fractional uncertainty

Answer 10

ratio of the uncertainty to the measured value

Question 11

percentage uncertainty

Answer 11

fractional uncertainty multiplied by 100

Question 12

SINGLE POINT example
In the meter shown below the smallest division for this meter is 0.2 volts.

Answer 12

• The uncertainty is ± 0.1 v
• The blue arrow on the meter represents 1.4 v ± 0.1v
• The absolute uncertainty is 1.4v ± 0.1v
• The relative uncertainty is .1 1.4 =0.07
• The fractional uncertainty is 0.07 x100=7%

Question 13

TWO-POINT example
To use a ruler to measure the length of the pencil we must determine the smallest division of the ruler.

Answer 13

Because the smallest division is 1 mm, the uncertainty is 0.5 mm. We must remember that there is uncertainty on each end of the ruler, so the uncertainty is 2 times the uncertainty (0.5 mm).
- The pencil is 2.6 cm ± 1 mm or 26 mm ± 1 mm
- The absolute uncertainty is 26mm ± 1mm
- The relative uncertainty is 1 26 =0.04
- The fractional uncertainty is 0.04 x 100=4%

Question 14

REPEATED example method 1
Because we have a set of repeated measurements, we can find the range and divide it by 2.

Answer 14

Maximum value = 83.4 dB SPL
Minimum value = 75.3 dB SPL
Range = 8.1 dB SPL
Uncertainty = 1/2 ∗8.1=4.05 dBSPL
- The absolute uncertainty is 78.8 dB SPL ± 4.1 dB SPL
- The relative uncertainty is 4.1/78.8 =0.05
- The fractional uncertainty is 0.05 x100=5%

Question 15

REPEATED example method 2- standard deviation
Because we have a set of repeated measurements, we can find the range and divide it by 2.

Answer 15

A second approach to expressing the uncertainty is to find the standard deviation or the variance
- variance is 6.1 and the standard deviation is 2.5
- measurement is 78.8 dB SPL ± 2.5 dB SPL.

Question 16

DIGITAL example
Thermometer

Answer 16

This is a digital thermometer and has an uncertainty of ± .1 degree. There is one place to the right of the decimal point.
- The measurement represented here is 23.6 deg ± 0.1 deg