Question

Distinguish between the terms accuracy and precision. In general, explain why a precise measurement does not always guarantee an accurate result.

Short answer

Accuracy is about closeness to the true value; precision is about consistency. Precise measurements aren't always accurate due to possible systematic errors.

Step-by-step solution

Define Accuracy

Accuracy refers to how close a measured value is to the true or accepted value. It is a measure of correctness and validity of a measurement.

Define Precision

Precision refers to the consistency of repeated measurements; how close the measurements are to each other, regardless of whether they are close to the true value or not.

Contrast Accuracy and Precision

While accuracy is about correctness and how close a measurement is to the actual value, precision is about the repeatability of measurements. A measurement can be very precise, consistently providing similar results, yet still not be accurate if all the measurements are far from the true value.

Example of Precise but not Accurate

Suppose a scale consistently measures the weight of a 500g standard weight as 450g. The readings are precise since they are consistently close to each other, but the measurements are not accurate since they are not close to the true value of 500g.

Conclusion on Precision and Accuracy

A precise measurement does not always guarantee an accurate result. Precision only ensures that repeated measurements give similar results; it does not account for systematic errors or calibration issues that affect accuracy.

Key concepts

Accuracy in measurements

Accuracy is an essential aspect of measurement that points to how close a measurement is to the actual or true value. Imagine you are throwing darts at a target. Accuracy would reflect how close your darts land to the bullseye, regardless of how many times you throw.
Accurate measurements are crucial in scientific experiments, engineering designs, and any field that relies on data. They ensure that conclusions drawn from data are valid and reliable.
This concept deals with reducing errors to ensure the measured values reflect reality more closely.

• Accuracy cannot be assessed without a known standard or "true" value.
• Errors affecting accuracy can be random or systematic.
• High accuracy implies low systematic error and small random errors.

Precision in measurements

Precision, often synonymized with reproducibility or consistency, measures how close the results are to each other on repeated trials, without necessarily being near the true value. Think back to our darts analogy: precision is achieved when your darts land closely together, but not necessarily near the bullseye.
Precision is vital in ensuring that measurements are repeatable and consistent. It is particularly important in experiments where consistency in results is required, even if those results are yet to be refined in terms of accuracy.

• Precision does not consider bias toward the true value.
• A precise measurement can still be inaccurate if there's a systematic error.
• High precision indicates good control of variables affecting measurements.

Systematic errors in measurements

Systematic errors are persistent biases or inaccuracies that cause the measurements to deviate in a consistent direction from the true value. These errors can significantly impact the accuracy of measurements.
Such errors often stem from faulty equipment, poor calibration, or errors in the experiment's design or execution.

• Unlike random errors, systematic errors are not reduced by repeated measurements.
• Common sources include instrument miscalibration and improper data analysis techniques.
• Identifying and correcting systematic errors is crucial to improving measurement accuracy.

Calibration in measurements

Calibration is the process of adjusting and correcting the measurements of an instrument to ensure it provides accurate readings. It involves comparing the output of the instrument with a known standard or reference.
A well-calibrated instrument reduces systematic errors and enhances both the accuracy and precision of measurements. Calibration is necessary in nearly all situations where precise and accurate measurements are vital.

• Regular calibration helps maintain instrument performance and reliability.
• It involves adjustments to align the instrument output with standards.
• Proper calibration can prevent systematic errors and misleading data.