Transcript Accuracy vs. Precision

Precision, Accuracy, and
Estimating Uncertainty
 What
is the difference?
PRECISION
ACCURACY
 Exactness
 Correctness
 Divisions
 Calibration
on scale
 Reproducibility
 Uncertainty
 Significant
digits
 Comparison
standard
 Error
 Technique
to a
 Estimate
and record one digit past the
smallest division on the scale when using
a non-digital scale.
 If digital, record all numbers in the
display.
 Use
whiteboards to display responses to
those problems assigned by McGreevey.
 Uncertainty
• Range within which you are certain the
measurement lies.
 Absolute
Uncertainty
• Uncertainty reported with the same units and
precision as the measurement itself
• Ex. 235 kg ± 2 kg or 14.03 cm ± 0.05 cm
 Percent
Uncertainty
• Uncertainty as a ratio to the measurement
• Ex.
2 𝑘𝑔
235 𝑘𝑔
= 0.0085 or 0.85%
 For
an individual non-digital
measurement:
• Consider between 1 and 5 in the estimated
place value (that’s one-tenth to one-half the
smallest division)
• Example: Measured value: 1.04 cm
Uncertainty: as low as ± 0.01
as high as ± 0.05
• Use your judgment in each circumstance to
increase or decrease the uncertainty.
• Don’t overestimate just to be “safe”.
 Use
whiteboards to display responses to
those problems assigned by McGreevey.
 For
an individual digital measurement:
• Make use of any uncertainty provided by the
manufacturer.
• If no uncertainty is provided, estimate ± 1 - ± 5
in the smallest place value displayed
 For
multiple measurements:
• Calculate the average, and then add ± :
 (Hi-Lo)/2 (see Physics Skills #10 packet)
 As the name implies, Highest value minus lowest value,
divided by 2
 Average Absolute Deviation (see Physics Skills #10 packet)
 The average of the absolute value of the differences
(deviations) of each individual measurement from the
average.
 When
adding or subtracting
measurements…
• The result is limited in precision by the least
precise measurement.
• Add the absolute uncertainties, if uncertainties
are in included.
 Example
•
0.50 cm ± 0.08 cm
Only one place past
decimal because of
30.2 cm
+ 30. 2 cm ± 0.1 cm
30.70 cm ± 0.18 cm = 30.7 cm ± 0.2 cm
Precision matches
that of the
measurement
 When
multiplying or dividing
measurements…
• The result is limited by the measurement with
the least significant digits.
• Add the percent uncertainties, if uncertainties
are included.
 Example
•
30.5 m ± 2.0%
x
Only 2 sig. figs.
because of 2.2 m
2. 2 m ± 1.5%
67.1 m2 ± 3.5 % = 67 m2 ± 3.5 % ( = 2 m2)
If converted to an absolute
uncertainty, precision matches that of
the measurement
 When
multiplying or dividing a
measurement by a number (as in an
equation)…
• Maintain the same number of significant digits
• Multiply or divide the absolute uncertainty by the
number
• OR maintain the same percent uncertainty.
 Ex:
radius = 3.0 mm ± 0.2 mm
Circumference = 2πr =
2π (3.0 mm ± 0.2 mm) = 19 mm ± 1mm
2 sf
2 sf
 When
raising a measurement to a power
(as in an equation)…
• Maintain the same number of significant digits
• Multiply the percent uncertainty by the power
 Ex:
radius = 3.0 mm ± 0.2 mm (6.7%)
Area = πr2 =
π (3.0 mm ± 6.7%)2 = 28 mm2 ± 13%
2 sf
2 sf