This document discusses measurements, errors, and precision vs accuracy in experimental science. It describes two main types of errors: random errors which are inevitable but can be minimized, and systematic errors which can be eliminated. Random errors result from unpredictable variations and can be reduced by taking multiple independent measurements. Systematic errors are associated with issues like improper instrument calibration, use of the wrong equipment or procedures. The document also explains that precision refers to the reproducibility of measurements but does not guarantee accuracy, which is defined as closeness to the true value.

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Measurements
and
Errors

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Physics
Experimental Science
Measurements
Certainties Uncertainties
Errors
Physics in strict sense…

3. Measuring the experimental Variables
Input
System
Output

4. Measuring the experimental Variables
Characteristics of Equipment
Accuracy Output
Complexity Range
Cost Reliability
Ease of Use Sensitivity
Longevity Units

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Types of Errors
a) Random Errors
- results from unknown or unpredictable variations in experiments
- These errors inevitable. They cannot be eliminated but can be
minimized.
Possible sources of random errors:
 Fluctuations of physical factors
 air temperature
 atmospheric pressure
 voltage / mechanical stability of the set-up
 friction in mechanisms

6. Analysis of Data
• Random errors – due to noise fluctuations
• Always present
• Can be minimize by having multiple measurements
How many measurements are needed?
– In manual measurements (10<N<20). Take note that
the measurements should be independent.
• Why not more?
– In automated measurements (N>>20)

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Types of Errors
b) Systematic Errors
- Errors that are associated with particular instruments or techniques.
- These errors can be eliminated.
Possible sources of systematic errors:
 instrument is not properly calibrated
 the graduation of the instrument deviates from the standard
 wrong instrument used
 wrong procedure

8. Analysis of Data
• Systematic errors – due to systems
– Accuracy of the system
• Uncalibrated
• Complexity
• Unreliable
• Out of range
• Use of inappropriate instrument
– Wrong usage of the measuring equipment's
• Did not follow manufacturer's specification
• Wrong assumptions

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Precision vs Accuracy

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Precision vs Accuracy

11. MEASURED VALUE

12. Dealing with pairs of variable

13. (x1,y1)
(x2,y2)
𝑠1 =
𝑦2 − 𝑦1
𝑥2 − 𝑥1
(x3,y3)
(x4,y4)
𝑠2 =
𝑦4 − 𝑦3
𝑥4 − 𝑥3
𝑠𝑎𝑣𝑒 =
𝑠1 + 𝑠2
2
∆𝑠 =
𝑠1 − 𝑠2
2