Test: Accuracy & Precision - JEE MCQ

Accuracy:

• It is the; closeness to the true value; closeness with which an instrument reading approaches the true or accepted value of the variable (quantity) being measured.
• It is considered to be an indicator of the total error in the measurement without looking into the sources of errors.

Precision:

• The most repeatable value (or) the reproducible value out of the set of records is known as precision.
• It is the measure of consistency. It gives the closeness of individual measured value to the average of all measured values.

For accuracy of the instrument, both conformity and precision are necessary.

Fidelity:- It is defined as the ability of system to reproduce the output in the same form as input.

It is the degree to which a measurement system indicates changes in measurement without any dynamic error.

Statement 2 is correct.

Statement 3 is correct.

Concept:

Accuracy

• The property of an instrument to measure the correct (accurate )value is said to be accuracy
• It also defined as the closeness of the measurement  to the standard or true value
• To distinguish between signal having very close values, we need an instrument with high accuracy

Accuracy: It is the closeness with which an instrument reading approaches the true value of the quantity being measured. It means conformity to truth.

It can be expressed in the following ways.

Point accuracy: This is the accuracy of the instrument only at a point on its scale. It doesn’t give information about the accuracy at any other point on the scale.

Accuracy as a percentage of scale range: When an instrument has a uniform scale, its accuracy can be expressed in terms of the scale range.

Example: The accuracy of a voltmeter having a range of 200 V may be expressed as ±1 percent of the scale range

±1 percent of scale range = 0.01 × 200 = 2 V, i.e. the reading will have ±2 V error.

Accuracy as a percentage of true value: While measuring we can express the accuracy of reading as a percentage of true value.

Example: The accuracy of a voltmeter having a full-scale range of 200 V and it is used to measure 20 V and the accuracy is ±1 percent of true value

True value = 20 V

±1 percent of true value = 0.01 × 20 = 0.2 V

Option (1) Explanation-The unit of measurement can be precise but not accurate. Precision is referred as the closeness of two measurements to one another while accuracy refers to the closeness of the measurement from the standard or known value. Precision is independent from accuracy and may not be accurate. So this statement is not correct.

Option (2) Explanation-Correctness in measurement require both  the closeness of the measurement from the standard or known value (accuracy) and Closed value of measurement (Precision). So this statement is correct.

Option (3) Explanation-Precision refers to the consistency of repeated results. The less the differences among repeated measures the larger the measurement precision. So this statement is correct.

Option (4) Explanation-Accuracy" refers to the difference between a measurement taken by a measuring tool and an actual value. The relative accuracy of a measurement can be expressed as a percentage; If a instrument  is 98 percent accurate, or that it is accurate within 2 percent. If a instrument  is 95 percent accurate, or that it is accurate within 5 percent. So yes 2 percent is better than 5  percent accuracy.

Concept:

Percentage error is a measurement of the discrepancy between an observed and a true, or accepted value.

Percentage error = (Expected value - Measured value)/ Expected value × 100

Relative Accuracy is how close a measured value is to a standard value on relative terms.

Relative Accuracy( in percentage) = (Measured value)/Expected value × 100

Calculation:

Given; 

Expected value = 80 V

Measured value = 79 V

Percentage error = (Expected value - Measured value)/ Expected value × 100

= (80 - 79)/80 × 100

= 1.25 %

Relative error = (Measured value)/Expected value × 100

= 79/80 × 100

= 98.75 %

= 0.9875

Accuracy:

• It is the; closeness to the true value; closeness with which an instrument reading approaches the true or accepted value of the variable (quantity) being measured.
• It is considered to be an indicator of the total error in the measurement without looking into the sources of errors.

Precision:

• The most repeatable value (or) the reproducible value out of the set of records is known as precision.
• It is the measure of consistency. It gives the closeness of individual measured value to the average of all measured values.

For accuracy of the instrument, both conformity and precision are necessary.

Some of the important characteristics of measuring instruments are specified by using the following terms:

Precision:

• It is a measure of the reproducibility of the measurements.
• Given a fixed value of a variable, precision is a measure of the degree to which successive measurements differ from one another i.e., a measure of reproducibility or agreement with each other for multiple trials.

Precision is composed of two characteristics: conformity and the number of significant figures to which measurement may be made.

• Conformity: It is the ability of an instrument to produce the same reading, or it is the degree of similarity between the individual measurements.
• So, it is also called repeatability or reproducibility and the number of significant figures. 

Mathematically, Precision is expressed as “the absolute maximum deviation from the average of the readings”, i.e.

Precision = max {(V_AV - V_MIN), (V_MAX - V_AV)}

Accuracy:

• It is the closeness to the true value; closeness with which an instrument reading approaches the true or accepted value of the variable (quantity) being measured.
• It is considered to be an indicator of the total error in the measurement without looking into the sources of errors.

Sensitivity: It the ability of the measuring instrument to respond to changes in the measured quantity. It is expressed as the ratio of the change of output signal or response of the instrument to a change of input or measured variable.

Resolution: It is the smallest change in measured value to which the instrument will respond, i.e. the smallest incremental quantity that can be reliably measured.
Error: It is the deviation from the true value of the measured variable.

Reproducibility:

• It is the degree of closeness with which a given value may be repeatedly measured. It may be specified in terms of units for a given period of time. Hence option (2) matches the definition of reproducibility i.e. it is the closeness of output readings for the same input when there are changes in the observer, locations, measuring instruments, etc.
• Perfect reproducibility means that the instrument has no drift.
• No drift means that with a given input the measured values do not vary with time.

Precision: It is the measure of reproducibility i.e., given a fixed value of a quantity, precision is a measure of the degree of agreement within a group of measurements.

• Precision of an instrument does not guarantees accuracy
• An instrument with more significant figures has more precision
• Deflection factor is reciprocal of sensitivity