Accuracy Precision Measurement

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.

Accuracy and Precision Definition

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:

1. 2.001 kg

2. 2.000 kg

3. 1.998 kg

4. 2.004 kg

5. 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:

1. 2.082 kg

2. 2.187 kg

3. 2.071 kg

4. 2.120 kg

The above set of measurements are human errors.

• Inaccurate & Precise

1. 1.824 kg

2. 1.834 kg

3. 1.828 kg

4. 1.825 kg

• Inaccurate & Imprecise

1. 0.525 kg

2. 3.828 kg

3. 0.906 kg

4. 5.252 kg

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Distinguish between Accuracy and Precision Class 11

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

Difference between Accuracy and Precision Answers

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

1. 573.4 ft

2. 575.3 ft

3. 565.2 ft

By Group Q:

1. 603.5 ft

2. 602.3 ft

3. 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 = 573.4+575.3+565.23

= 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 = 603.5+602.3+596.73

= 600.8 or 601 ft

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

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?

1. Accurate & Precise

2. Accurate & Imprecise

3. Inaccurate & Precise

4. Inaccurate & Imprecise

Solution: We are given the following data:

1. 262.2 m

2. 261.1 m

3. 259.3 m

4. 258.7 m

On doing the average of these numbers, we get:

262.2+261.1+259.3+258.74

= 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.

What is False Precision?

• Madsen Pirie has defined "false precision" as, when exact numbers are used to express precision that cannot be expressed in exact terms/ or have not been actually measured through the instrument. In day to day life, this can be understood through examples like, "From here, 90% of the complexity in an exam is getting started." Another example is "our food product is twice as healthy as our competitor's". One might find that false precision is exploited to create an unwarranted confidence in many marketing claims as discussed.

• In the field of science and engineering, convention dictates that unless a margin of error is explicitly stated, the number of significant figures (including the numbers after a decimal point) used in the presentation of data should be limited to what is actually revealed during precision measurements of those data. For example, if an instrument can be read to tenths of a unit or up to two decimal places of measurement, results of calculations using data obtained from that measuring device can only confidently state the precision to the tenths place or two decimal values, regardless of what the raw calculation returns or whether other data used in the calculation are more accurate.

• In the scientific community, there is a criteria which states that all the non-zero digits of a number are meaningful. Hence, if one falsely provides excessive figures, it may lead the evaluators to expect better precision than really found in the experiment.

• However, contrary to this practice, it is advised to not round up figures and retain more significant figures than this in the intermediate/ calculation stages, so that errors arising due to the rounding off of figures can be avoided.

• It has been found that in most experiments, unintended false precision can creep in if both the high-precision and low-precision data are combined together, because there can be inequality in conversion of units.

Quantification of Data

Quantification of data through accuracy and precision In industrial instrumentation is necessary. In most cases, a measurement device is designed to be both accurate and precise so that they produce measurements that are close to each other and tightly clustered around the true value of an experimental variable. The accuracy and precision of a device is usually established by measuring some traceable reference standard multiple times during the process.

With regard to accuracy:

We can differentiate between the mean of the measurements and the reference value, to obtain the bias. In instrumentation, establishing and correcting the bias is necessary during calibration.