Given below are two statements: Statement I: The standard deviation of a…
2023
Given below are two statements:
Statement I: The standard deviation of a series of repeated measurements estimates the likely size of the chance error in a single measurement.
Statement II: Bias affects all the measurements in the same way, pushing them in the same direction.
In the light of the above statements, choose the correct answer from the options given below.
Answer: A. Both Statement I and Statement II are true — ConceptRandom (chance) error varies unpredictably among repeated measurements, whereas systematic error creates a repeatable displacement. Bias is the…
- A.
Both Statement I and Statement II are true
- B.
Both Statement I and Statement II are false
- C.
Statement I is true but Statement II is false
- D.
Statement I is false but Statement II is true
Attempted by 2 students.
Show answer & explanation
Correct answer: A
Concept
Random (chance) error varies unpredictably among repeated measurements, whereas systematic error creates a repeatable displacement. Bias is the systematic component—the offset of a measurement process from the reference value.
The standard deviation of repeated results quantifies their dispersion and therefore estimates the random-error scale of a single measurement; the uncertainty of the mean would instead be s divided by the square root of n.
Application
Statement I connects the standard deviation of repeated measurements with the likely chance error in one measurement. This is the standard interpretation of repeatability dispersion, so Statement I is true.
Statement II describes bias as a systematic effect that shifts the measurements in a common direction. This is the defining behavior of systematic error, so Statement II is true.
Contrast
‘Both Statement I and Statement II are false’ discards both established distinctions between random dispersion and systematic displacement.
‘Statement I is true but Statement II is false’ identifies the role of standard deviation but misclassifies the directional nature of bias.
‘Statement I is false but Statement II is true’ recognizes bias as systematic but rejects the use of repeated-measurement spread to estimate chance error.
Cross-check and result
A repeated series can be tightly clustered yet displaced from the reference value: standard deviation captures the random spread, while the common displacement is bias. Therefore, both Statement I and Statement II are true.