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Precision of a measurement depends on the size of the smallest measuring value because the smaller the measured unit of the instrument, the greater will be the accuracy of a measured value. The precision of a measurement is a measure of the degree of agreement among a variety of measurements of the same quantity. Simply, it reflects how consistent and reproducible a measurement is.
- A measurement is known to be precise if it produces similar results each time it is taken. It can be expressed in terms of the number of significant figures in a measurement.
- Accuracy and precision are two very essential factors to consider in measurement.
- Accuracy refers to the closeness of a measured value to its true value.
- It can simply be defined as the degree of agreement between the measured value and the true value of the quantity that is measured.
- An accurate measurement is one very close to the true value, while an inaccurate measurement is one that is far from the true value.
Read Also: Uncertainty in Measurement
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Key Terms: Accuracy, Precision, Relative Deviation, Absolute Deviation, Relative Error, Absolute Error, Percentage, Variation, Standard Deviation, Error, Units and Measurements
What is Precision?
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Precision is the measure of how close multiple measurements of the same quantity are to each other, regardless of whether those measurements are close to the true or accepted value.
- It can be expressed as a measure of reproducibility, or how consistent and repeatable a measurement is.
- Precise measurements are ones that consistently yield equivalent results when repeated multiple times.
- This is often expressed in terms of the number of significant figures in the measurement
- For example, if any given substance is weighed five times successively and each time you get the same value of 6.4 kg then the measurement is said to be Precise.
It represents how well a measurement is repeated or reproduced under the same conditions. It is typically used to evaluate how reliable a measurement is. A measurement that has a high level of precision has a narrow range of values that are very close to one another, while a measurement that has a low level of precision has a wider range of values that are more spread out. Precision is usually expressed as a standard deviation or a percentage of error.
Significant Figures Video Lecture
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| Measurement of length | Sampling Error | Cisplatin |
| Uses of Vernier Calipers | Absolute and Relative Error | Dimensional Analysis |
What is Accuracy?
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Accuracy indicates how close a measured value is to the true value. It can be defined as a measure of the degree of conformity between a measured value and a quantity's true value.
- It is usually represented as a percentage or as an absolute value.
- For example, if any given substance, by weighing it you gain a measurement of 6.2 kg but the actual or standard value of that particular substance is 10 kg then the measurement is said to be inaccurate.
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An accurate measurement is one that is free from systematic errors and has a low random error, which means that the measured value is very close to the true value
Note: Scientifically, Precision in measurement is independent of the term accuracy. As said often, in a given data you can be precise but inaccurate at the same time.
Fig. Accuracy
In other words, you can be accurate but imprecise in the measurement. Also, Accuracy and Precision, are sometimes used conversely in taking the measurements but they possess very definite definitions in terms of science. The degree of accuracy and precision are dependent on the measuring instrument by which the measurement is taken.
Examples of Precision and Accuracy
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Example 1
If the basketball player throws the ball with proper accuracy, he always wanted to take the ball close or into the basket. If the basketball player throws the ball with full precision, he will aim to take the ball to the area which may be the basket or nearly close to the basket.
It is to be noted here that a good basketball player will be both accurate and precise in throwing the ball at every time and each time it will try to make the ball in the basket.
Fig. Example of Precision and Accuracy
Example 2
If we take the examples of dart boards, hitting the target accurately in the dart boards implies that you are very close to the centre of the target, regardless of whether all the marks are on different sides to the centre.
Hitting the target precisely on dart boards, signifies that all the hits are close to each other irrespective of the result that they are very far from the centre of the target.
Fig. Precision and Accuracy: Dart Board Example
Example 3
Taking the example of thermometer:
If in a mercury thermometer, the temperature of the hot cup reading shows is 60 degrees celsius and the actual value of that cup is also 60 degrees celsius then it is said to be accurate.
If the thermometer reading constantly shows the temperature at 50 degrees celsius then it is said to be precise regardless of the actual value.
Also Read: Thermal Conductivity of Copper
Definition of Measurement
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Measurement is defined as the determination of the size or magnitude of the given matter and by comparing it with the other material with some standard quantity of the same kind.
- In normal cases in a particular instrument, you have to take a measurement fractionally between two definite measurements.
- Measurement is simply a process of determining the value or quantity of a physical quantity, such as length, mass, temperature, time, etc., using appropriate measuring instruments or techniques.
- We are required to evaluate the measuring instrument very precisely while making the measurements of a particular object.
- In order to avoid error while measuring the substance smaller in size you need to use equipment that will be more precise.
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Difference between Accuracy and Precision
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The Differences between Accuracy and Precision are:
| Accuracy | Precision |
|---|---|
| Accuracy is when the values are too close to the actual value on measurement | Precision is when the values repeated are the same in the measurement, irrespective of the actual value |
| Measurement can be accurate but not considerably precise. | Measurement can be precise but not compulsory accurate. |
| It can be gained in a single measurement. | It can be determined by taking multiple measurements. |
| It can have systematic errors. | It can have an error randomly during measurements. |
| The values which are accurate are precise in normal cases. | The values which are precise may or may not be accurate. |
| Accurate values can be improved after measurements. | Precise values cannot be improved after measurements. |
| The values which are accurate are independent of precision. | The values which are precise are independent of accuracy. |
Learn in Detail: Difference Between Accuracy and Precision
Things to Remember
- The result of a measurement is expressed in terms of a numerical value and a unit.
- Units of measurement are standardized quantities used to express the magnitude of a physical quantity, such as meters for length, seconds for time, and kilograms for mass.
- As per the context of measurements, accuracy indicates how close a measurement is to its true or accepted value.
- Precision refers to the closeness of two or more measurements to each other or the repeatability of a single measurement.
- Accuracy refers to the closeness of a measured value to a known or true value, while precision refers to the reproducibility or consistency of a measurement.
- In an example, Accuracy refers to how close the darts are to the bullseye, while precision refers to how close the darts are to one another.
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Previous Year Questions
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Sample Questions
Ques. The actual quantity of liquid is measured at 30 litres. If a student measures the quantity of the liquid to be 26 litres, 25 litres, 26.5 litres, and 25.3 litres in the successive trials respectively. Find if the data is accurate or precise. (1 mark)
Ans. The above given data shows us that the actual quantity of liquid is measured as 30 litres. As the students measured the quantity in four successive trials to be 26 litres, 25 litres, 26. 5 litres and 25.3 litres respectively is referred to as good precision because regardless of the actual measured value the other four values are close to each other. So, the final conclusion of the above question is that it is a good precision.
Ques. Define the statement if the measurement is repeatable and consistent. (1 mark)
Ans. If in a given data the measured value in number of attempts is repeating or consistently showing the close figures then the value is said to be in High Precision because precision depends on the outcome values irrespective of the actual or standard value provided in the question. Highly precise values always show the closeness among the following values which we get in 3 to 5 attempts.
Ques. The actual weather forecast was 35-degree celsius. A news channel forecasted the values 33-degree celsius, 34-degree celsius, 35-degree celsius, and 36-degree celsius successively in the four different trials respectively. Answer the correct statement for the question. (1 mark)
Ans. The actual forecast of weather phenomena gives the value of 35-degree celsius but the other forecasted values followed by it four times provide the values 33-degree celsius, 35-degree celsius, 36-degree celsius, and 34-degree celsius which is clearly a high precision value no matter what will be an actual forecast of weather, the data is said to be in High Precision.
Ques. The length of the train is 380 metres. A man measures the length of the train to be 381 m, 382 m, 381.5m, 380.6 m, and 381.4 m in the first, second, third, fourth and fifth trails respectively. Which statements correctly depict the answer of the following questions? (2 marks)
Ans. The above question depicts the clear case of the data to be not only in High Precision but also High accuracy as notwithstanding the actual or standard values of the length of the train is (380 metres).
The multiple attempts (381 m, 382 m, 381.5m, 380.6 m, and 381.4 m) clearly show the closeness of the values. Therefore, it is the condition of both High Precision and High Accuracy.
Ques. Define the statement the precision in a measurement depends on the least reading of the measuring instrument. (2 marks)
Ans. As we know that small readings in a measurement is due to smaller measurement on a measuring instrument therefore it implies that smaller readings will lead to better precision in a measured value.
For example: The least normal ruler reading is 1mm while it is 0.1mm in vernier callipers also in other words it will give a reading of 10-3 cm, which is referred as 0.1 mm < 1mm.
Therefore, vernier callipers will be more precise and more accurate in measuring anything.
Ques. Write a short note on Reproducibility. (3 marks)
Ans. Reproducibility refers to the ability to obtain consistent or similar results in repeated experiments or measurements, typically by different researchers or with different instruments or methods, under similar conditions.
- In scientific research, reproducibility is a fundamental requirement to validate the findings of a study and ensure that the results are reliable and can be trusted.
- To achieve reproducibility, it is important to carefully control the variables that could influence the outcome of an experiment or measurement.
- This involves using standardized methods and procedures, ensuring that equipment is calibrated and operating correctly, and minimizing sources of error that could affect the accuracy and precision of the results.
Apart from controlling the experimental conditions, it is equally vital to document the methodology and results of the experiment in a clear and brief manner in order for other researchers to understand the process and attempt to reproduce the findings.
Ques. Classify Accuracy of the system. (2 marks)
Ans. Accuracy of the system can be divided into three parts, namely:
- Point Accuracy
- Accuracy as Percentage of Scale Range
- Accuracy as Percentage of True Value
Ques. What is Error? (2 marks)
Ans. In physics, error defines the difference between the true value or the theoretical value and the measured or experimental value. It is the deviation or the “mistake” that occurs during a measurement or experiment. The error can occur due to various reasons such as limitations of the measuring instrument, human error, environmental factors, or inaccuracies in the experimental setup. The goal of reducing the error is to increase the accuracy and precision of the measurement or experiment.
Ques. What is Point Accuracy? (1 mark)
Ans. The accuracy of the instrument, on its scale, which is only at a particular point is called point accuracy.
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