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We know that the measuring process is fundamentally an operation of comparison, and to measure any physical quantity, we compare it with a standard unit of that quantity.

We also know that no measurement is perfect, so the difference between the accepted value and the measured value of the quantity is called the error of measurement. To overcome this, we have introduced the two terms ‘Accuracy and Precision’.

Accuracy and Precision reflect how close our measurements are to the accepted value. In this article, we will understand these two terms in detail.

While dealing with physics, we do many experiments, and for doing experiments, we collect data. If the data is quantitative, we must learn the concepts of accuracy and precision to analyze the data. Now, let’s define these two terms and discuss how they apply to sets of numbers.

Accuracy in Physics

Accuracy implies how close the data is to the accepted value of something. Like, if we measure the mass of object ‘A’ as 2.011 kg on our balance, while precisely it was 2 kg. Here, we can say that we got a very accurate measurement because the measured value is close to the accepted value.

Precision

The word ‘Precision’ refers to the closeness of the numbers in a given set of data.

For example, while measuring the mass of an object ‘A’ on different measuring instruments, we get the following set of data:

2.001 kg

2.000 kg

1.998 kg

2.004 kg

2.010 kg

We can say that it is a highly precise data set because all these values are very close to the accepted value. However, if there were variance in the data, we would say it was imprecise.

From the above example, we can comprehend that the data set can be both accurate and precise, which means ‘Good Measurement.’ Other factors may arise during the measurement; these are:

Accurate & Imprecise

For the following data set of measurements, we have:

2.082 kg

2.187 kg

2.071 kg

2.120 kg

The above set of measurements are human errors.

Inaccurate & Precise

1.824 kg

1.834 kg

1.828 kg

1.825 kg

Inaccurate & Imprecise

0.525 kg

3.828 kg

0.906 kg

5.252 kg

Now, let’s see the accuracy and precision examples.

Question 1: Let’s say the distance between points A & B is 600.0 ft. In an experiment performed by two groups P and Q, the measurement values are as follows:

By Group P

573.4 ft

575.3 ft

565.2 ft

By Group Q:

603.5 ft

602.3 ft

596.7 ft

Check whether the measurements of groups P and Q are accurate & Precise or not.

Solution:

Group P

Let’s find the average of the data set:

= \[\frac{573.4 + 575.3 + 565.2}{3}\]

= 571.3 ft, which isn’t close to the accepted value, i.e., 600 ft. However, the data set has precise values.

So, we can say that the measurement done by group P is accurate but not precise.

Group Q

= \[\frac{603.5 + 602.3 + 596.7}{3}\] = 600.8 or 601 ft

Here, the value is accurate, and the data set is precise.

Question 2: The length of the model is 260 m. A girl measures its length and finds it to be 262.2 m, 261.1 m, 259.3 m, and 258.7 m in the first, second, third, and fourth trials, respectively. Which among the following statements is correct for her measurements?

Accurate & Precise

Accurate & Imprecise

Inaccurate & Precise

Inaccurate & Imprecise

Solution: We are given the following data:

262.2 m

261.1 m

259.3 m

258.7 m

On doing the average of these numbers, we get:

\[\frac{262.2 + 261.1 + 259.3 + 258.7}{4}\]= 260.35 m

We can see that the value of 260.35 m is close to the correct value, i.e., 260 m, and the set of data mentioned above is precise.

Therefore, we can say that the above data is both accurate and precise. So option (a) is correct.

FAQ (Frequently Asked Questions)

Question 1: Why is Precision more important than Accuracy?

Answer: The statement Precision is more important than Accuracy seems ambiguous as we use both these terms interchangeably. Now, let us clear this confusion by the following example:

I went to the market to purchase some amount of sugar. Every time, the balance used by the shopkeeper showed different measurements, i.e., 2.859 kg, 3.056 kg, 2.986 kg, 2.999 kg. The shopkeeper asked me to pay money for 3 kg of sugar. Though these measurements seem accurate, therefore, I used different devices to measure its weight and confirmed that the values were precise.

Question 2: What are the core parts of the Precision?

Answer: The following are the core parts of precision:

Repeatability: In this process, for measuring any quantity, we use the same device or instrument repetitively.

Reproducibility: The same object is measured using multiple devices or instruments.

Question 3: Are accuracy and Precision dependent on each other?

Answer: No, they are independent.

For accuracy, we can be satisfied with one value. However, for precision, we need to look for multiple values to find closeness among the given values.

Question 4: What is absolute Precision?

Answer: Absolute value describes the uncertainty in quantity. For example, the population growth in the coming years is 30% ± 15%. Here, the absolute uncertainty is 15%.