Mada za sehemu hiiUse various instruments to carry out measurements in physicsMada 2
- Use various instruments to carry out experiments in mechanics, vibrations and waves, thermal properties of materials and electrostatics
- Analyse the precision and accuracy of measurements
Precision and Accuracy in Measurements
Precision and accuracy are two fundamental concepts in experimental physics that describe the quality of measurements, but they have distinct meanings that should not be confused.
Precision refers to the closeness of two or more measurements to each other. If you measure a quantity several times and obtain very similar values each time, your measurements are precise. Precision is determined by the smallest scale division or least counting unit of the measuring instrument—the smaller the scale division, the greater the precision. For example, a micrometer caliper with a least count of 0.01 mm is more precise than a ruler with a 1 mm division.
Accuracy is the measure of how close a measured value is to the true or accepted value of the quantity. Accuracy depends on factors such as personal errors, imperfections in measurement techniques, instrumental errors, and environmental conditions like temperature, wind, and humidity.
A simple analogy helps distinguish them: a tennis player who consistently hits the same spot on the court (even if not near the target) is precise but not accurate. A player who hits around the target but scattered everywhere is accurate on average but not precise. The ideal is both accurate and precise.
The following methods help improve accuracy in measurements:
- Use instruments with the highest precision available (smallest possible unit)
- Apply correct techniques when using measuring instruments and reading values
- Avoid parallax error by taking readings while looking at a right angle to the scale
- Repeat the same measurement several times to obtain a reliable average value
- Take measurements under controlled conditions to minimize environmental influence
A student measures the acceleration due to gravity (g) three times and obtains values of 9.6 m/s², 9.8 m/s², and 9.7 m/s². The accepted value is 9.8 m/s².
Analysis:
- Mean value: (9.6 + 9.8 + 9.7) ÷ 3 = 9.7 m/s²
- Precision: The three measurements are very close to each other, indicating high precision
- Accuracy: The mean value (9.7 m/s²) is close to the accepted value (9.8 m/s²), indicating good accuracy
Another student obtains values of 10.2 m/s², 10.5 m/s², and 10.8 m/s². These measurements are precise (close to each other) but not accurate (far from the accepted value).
The minimum uncertainty in a direct measurement from a measuring device equals half of the smallest readable graduation on the scale. This is called the least count.
For a meter ruler with millimeter markings (smallest division = 1 mm):
- Uncertainty = ±0.5 mm = ±0.0005 m
For a digital stopwatch reading to 0.01 s:
- Uncertainty = ±0.005 s (if no other factors considered)
A measurement agrees with an accepted value if the accepted value falls within the measurement's uncertainty bounds.
Example: The accepted value of g is 9.8 m/s².
- Measurement A: 9.6 ± 0.3 m/s² → Range: 9.3 to 9.9 m/s². Since 9.8 lies within this range, the measurement agrees with the accepted value.
- Measurement B: 9.2 ± 0.3 m/s² → Range: 8.9 to 9.5 m/s². Since 9.8 is outside this range, the measurement does not agree.
| Aspect | Precision | Accuracy |
|---|---|---|
| Definition | Closeness of measurements to each other | Closeness of measurement to true value |
| Depends on | Instrument's least count | Instrument quality, technique, environment |
| Improved by | Finer scale divisions | Calibration, correct technique, averaging |
In Tanzanian everyday life, understanding precision and accuracy matters when using measuring instruments for practical tasks. For example, when a farmer in Mwanza uses a measuring tape to determine the amount of fertiliser needed per square metre of a rice paddy, using a tape with millimetre markings (higher precision) instead of one marked only in centimetres ensures more consistent application rates, leading to better crop yields. Similarly, when buying petrol at a filling station in Dar es Salaam, the accuracy of the pump meter ensures the customer gets the correct amount of fuel for their money.
Swali
What is the main difference between accuracy and precision in measurement?
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