measurement-and-data-processing-errors-and-uncertainties.ppt

Cómo calcular errores de medida en laboratorio de cualquier tipo sobre todo en alimentos

1. Errors and Uncertainties

2. •Every measurement has an associated
uncertainty or error.
•The uncertainty is an estimate of the amount it
can be off from the “true value”. It is as
important as the measurement itself. E.g. 2.0cm
+/-0.05cm
•If a medical thermometer had an uncertainly of
3
o
C it would be useless in determining whether a
person has a fever or not.
•An error is NOT the same thing as a mistake in
chemistry.

3. random and systematic
•A systematic error causes measurements to be
spread about a value rather than being spread
about the true value. It is a system or instrument
error:
•Badly made instruments
•Poorly calibrated instruments
•An instrument having a zero error.
•Poorly timed actions
•Instrument parallax error.

4. random and systematic
•Random Uncertainties are caused by variations
in the performance of an instrument or person.
•Change in the surroundings
•Misreading scales
•Variations in the thickness of a surface being
measured (eg thickness of a wire).
•Not collecting enough data (statistical error)
•Human parallax error

5. Repeated readings
•Many readings will help to reveal a random
error, but also help to reduce it. They cannot
reduce systematic errors

6. Accuracy and Precision
•Accuracy is how close a measurement is to the
true value (shown by the relative or percentage
error in the measurement.)
•Precision shows if a number of measurements
agree (indicated by absolute error).
•AN ACCURATE EXPERIMENT HAS A SMALL
__________ ERROR, A PRECISE EXPERIMENT
HAS A SMALL __________ ERROR.

7. Accuracy and Precision
•Accuracy is how close a measurement is to the
true value (shown by the relative or percentage
error in the measurement.)
•Precision shows if a number of measurements
agree (indicated by absolute error).
•AN ACCURATE EXPERIMENT HAS A SMALL
SYSTEMATIC ERROR, A PRECISE EXPERIMENT
HAS A SMALL RANDOM ERROR.

8. •The limit of reading of a
measurement is equal
to the smallest
graduation of the scale
of an instrument.
•The degree of
uncertainty of a
measurement is equal
to half the limit of
reading.

9. Common Uncertainties
•Metre Rule  0.5 mm
•Vernier Calipers  0.05 mm
•50 cm
3
measuring cylinder  0.1 cm
3
•10 cm
3
measuring cylinder  0.05 cm
3
•Electric Balance 0.005 g
•Watch second hand  0.5 s

10. Uncertainty range
•If the value of a measurement is written as:
2.3  0.1 cm, then the uncertainty range is
between 2.4 (2.3 + 0.1) and 2.2 (2.3 –0.1) cm.

11. UNCERTAINTIES IN CALCULATED
RESULTS

12. •Percentage uncertainty is the relative
uncertainty multiplied by 100 to give a
percentage (%)
= relative uncertainty  100%

13. 9.8  0.05 m
•Limit of reading = 0.1 m
•Uncertainty = 0.05 m
•Absolute uncertainty = 0.05 m
•Relative uncertainty = 0.05 m / 9.8 m =
0.005
•Percentage uncertainty = 0.005  100% = 0.5
%

14. ADDITION AND
SUBTRACTION INVOLVING
ERRORS
When adding measurements, the error is the sum of all the
absolute errors in each measurement.
Example: The sum of 2.6  0.5 cm and 2.8  0.5 cm is 5.4
 1.0 cm
When subtracting measurements, ALSO add the absolute
errors

15. MULTIPLICATION
INVOLVING ERRORS
When multiplying and dividing, add the relative
or percentage errors of the measurements
being multiplied/divided. The absolute error is
then the fraction or percentage of the most
probable answer.

16. MULTIPLICATION
INVOLVING ERRORS
e.g. calculation of volume
length L = 5.56 +/- 0.14 meters
= 5.56 m +/- 2.5%
width W = 3.12 +/- 0.08 meters
= 3.12 m +/- 2.6%
depth D = 2.94 +/- 0.11 meters
= 2.94 m +/- 3.7%
V =L*W*D=(5.56m)*(3.12m)*(2.94m)= 51.00 m
3
ERROR = 2.5% + 2.6% + 3.7% = 8.8%
ANSWER = 51.00 m
3
+/-

8.8% BUT (51.00 m
3
) * (8.8%) = 4.49 m
3
= 51.00 m
3
+/- 4.49 m
3