Can a measurement be precise but not accurate?

Absolutely, this is a common scenario. Imagine a weighing scale that is consistently off by $2, ext{kg}$ – it always reads $2, ext{kg}$ higher than the actual weight. If you weigh an object multiple times, and it consistently shows $102, ext{kg}$, $102.1, ext{kg}$, $102, ext{kg}$, while the true weight is $100, ext{kg}$, your measurements are precise (they are close to each other) but inaccurate (they are far from the true value). This usually indicates a systematic error in the measuring instrument or method.

Can a measurement be accurate but not precise?

Yes, this is also possible. Consider a situation where you are trying to measure the length of a rod, and due to various random factors like slight changes in your viewing angle, temperature fluctuations, or minor vibrations, your readings are $10.0, ext{cm}$, $10.5, ext{cm}$, $9.8, ext{cm}$, $10.2, ext{cm}$. If the true length of the rod is $10.1, ext{cm}$, then the average of your readings might be very close to $10.1, ext{cm}$, making your overall measurement accurate. However, the individual readings are quite spread out, indicating low precision. This scenario points to significant random errors.

What is the role of 'least count' in precision?

The least count of a measuring instrument is the smallest value that can be measured by it. For example, a standard ruler has a least count of $1, ext{mm}$ or $0.1, ext{cm}$. A vernier caliper might have a least count of $0.01, ext{cm}$, and a screw gauge $0.001, ext{cm}$. A smaller least count means the instrument can distinguish between finer differences in measurement, thus allowing for more precise readings. The precision of a measurement is directly limited by the least count of the instrument used.

How do systematic and random errors relate to accuracy and precision?

Systematic errors primarily affect the accuracy of a measurement. They cause a consistent deviation of the measured values from the true value, shifting all readings in one direction. For example, a zero error in an instrument leads to inaccurate readings. Random errors, on the other hand, primarily affect the precision of a measurement. They cause unpredictable variations in individual readings, leading to a spread in the measured values around an average. Minimizing systematic errors improves accuracy, while minimizing random errors improves precision.

Why is it important to achieve both high accuracy and high precision in experiments?

Achieving both high accuracy and high precision is the ultimate goal in any scientific experiment because it ensures the reliability and validity of the results. High accuracy means your measurements are close to the true value, making them 'correct'. High precision means your measurements are reproducible and consistent, making them 'reliable'. Without both, your experimental findings might be misleading. For instance, a precise but inaccurate drug dosage could be harmful, and an accurate but imprecise measurement in research might not be reproducible by other scientists, hindering scientific progress.

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Accuracy and Precision

Physics

NEET UG

Version 1Updated 22 Mar 2026

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Accuracy refers to the closeness of a measured value to the true or accepted value of the quantity. It indicates how correct a measurement is. Precision, on the other hand, refers to the closeness of two or more measurements to each other, irrespective of their closeness to the true value. It reflects the reproducibility and resolution of a measurement. A measurement can be precise without being a…

Quick Summary

Accuracy and precision are fundamental concepts in understanding the quality of physical measurements. Accuracy refers to how close a measured value is to the true or accepted value of the quantity. It addresses the 'correctness' of a measurement and is primarily affected by systematic errors, which cause consistent deviations.

Precision, conversely, describes how close multiple measurements of the same quantity are to each other, reflecting the reproducibility and resolution of the measurement. It addresses the 'consistency' of a measurement and is primarily affected by random errors, which cause unpredictable variations.

An instrument's least count directly influences the precision it can achieve. It's crucial to understand that a measurement can be precise without being accurate, and accurate without being precise. The ideal experimental outcome is to achieve both high accuracy (minimal systematic error) and high precision (minimal random error) to ensure reliable and valid scientific data.

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Key Concepts

Accuracy vs. True Value

Accuracy is fundamentally about how well a measurement aligns with the 'true' or accepted value of a…

Precision and Reproducibility

Precision focuses on the consistency and reproducibility of measurements. If you repeat a measurement…

Least Count and its impact on Measurement

The least count (LC) of an instrument is the smallest division it can measure. It directly dictates the…

Accuracy: — Closeness to true value. Affected by systematic errors.

A propto \frac{1}{|\text{Measured} - \text{True}|}

Precision: — Closeness among repeated measurements. Affected by random errors, least count.

P propto \frac{1}{\text{Spread of readings}}

Systematic Errors: — Consistent, predictable deviations (e.g., zero error, faulty calibration). Affect accuracy.

Random Errors: — Unpredictable fluctuations (e.g., reading variations). Affect precision.

Least Count: — Smallest measurable value by an instrument. Smaller LC

implies

Higher Precision.

All Correct, Precise Repeaters!

Accuracy: Correctness (close to true value).

Precision: Repeaters (close to each other).

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