R5 Errors and Uncertainty Flashcards
What are the types of Error?
-Systematic Error
-Human Error
-Random Error
What is systematic error?
Errors where the measurement is always shifted up or down from the true value by the same amount.
What are the sources of systematic error?
-Zeroing errors (Not setting equipment such as a voltmeter or ammeter to 0 when the input is 0)
-Calibration Error
How to reduce systematic error?
-Careful calibration of equipment before you make a measurement
What is human error?
Mistakes caused by using equipment or implementing experimental techniques incorrectly
How to reduce human error?
-Repeat measurements and take an average
-Use digital measurements when possible
-Measuring scales at eye level
What is random error?
Random error refers to unpredictable variations in measurements that arise from factors that vary randomly each time a measurement is taken
What is accuracy?
Refers to the closeness of a measured value to the standard or known value
What is precision?
Precision is the closeness of several measurements with eachother
What is absolute error?
The difference between the measured value and the actual error
Formula for absolute error
Measured Value-Actual Value
Percentage relative error (Absolute error)
(Absolute Error/Actual Value) x100
How to calculate uncertainty using range?
-Calculate the range of Data
-Divide the range by 2
Range = 2.56 – 2.52 = 0.04 cm
* Use the range to find the uncertainty:
Uncertainty = Range ÷ 2 = 0.04 ÷ 2 = 0.02 cm
* So the uncertainty of the mean is:
2.53 cm ± 0.02 cm
Difference between Error and Uncertainty?
An error is the difference between the measured value and the known value
Uncertainty is an estimate of the range between them showing the reliability
How to find uncertainty from a resolution?
The smallest digit that the equipment that the equipment can measure
-For example, the equipment below can measure down to 2 decimals of
gram, therefore the uncertainty for this equipment is ± 0.01 g.
* The final result can be written as: 12.68 g ± 0.01 g
How to find uncertainty from a reading and you dont know what equipment that was used?
You take the last figure of the value and assume it is 1
-For example 5.27V -> Uncertainty=0.01
Adding or subtracting uncertainties?
-Combine the values of the uncertainties
-Combine the measured values
ex:
2.4cm (+-) 0.1
4.4cm (+-) 0.2
2.4+4.4=6.8cm
0.1+0.2=0.3
6.8 (+-) 0.3
Multiplying or dividing uncertainty?
-Convert absolute uncertainty to relative percentage uncertainty
-Multiply/divide the measured values
Multiply the percentage with the values
ex:
2.4cm (+-) 0.1
4.4cm (+-) 0.2
2.4X4.4=10.56cm^2
0.1/2.4 x100=4.16%
0.2/4.4 x 100= 4.54%
4.16%+4.54%=8.7%
10.56cm^2x8.7%=0.91
10.56 (+-)=0.91
When to use error or uncertainty
An error is the difference between the known value and the measured value
Uncertainty is an estimate of the range between them
Uncertainty from resolution?
Most of our measuring devices in this lab have scales that are hard for
our eyes to measure.
* For example, when measuring the length of an object against a meter
stick marked in centimetres as shown below, we can say that our result is
somewhere between 46.4 cm and 46.6 cm.
* We assume as an upper bound of our uncertainty, an amount equal to
half of this width: 46.6 cm – 46.4 cm = 0.2 cm, then 0.2 cm ÷ 2 = 0.1 cm.
* The final result can be written as: 46.5 cm ± 0.1 cm
