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# Why is a Set of 100 Measurements of the Diameter Expected to Yield a More Reliable Estimate than a Set of 5 - Physics

ConceptAccuracy Precision of Instruments and Errors in Measurement

#### Question

The mean diameter of a thin brass rod is to be measured by vernier callipers. Why is a set of 100 measurements of the diameter expected to yield a more reliable estimate than a set of 5 measurements only?

#### Solution 1

A set of 100 measurements is more reliable than a set of 5 measurements because random errors involved in the former are very less as compared to the latter.

#### Solution 2

Due to random errors, a large number of observation will give a more reliable result than smaller number of observations. This is due to the fact that the probability (chance) of making a positive random error of a given magnitude is equal to that of making a negative random error of the same magnitude. Thus in a large number of observations, positive and negative errors are likely to cancel each other. Hence more reliable result can be obtained.

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#### APPEARS IN

NCERT Solution for Physics Textbook for Class 11 (2018 to Current)
Chapter 2: Units and Measurements
Q: 8.3 | Page no. 35
Solution Why is a Set of 100 Measurements of the Diameter Expected to Yield a More Reliable Estimate than a Set of 5 Concept: Accuracy Precision of Instruments and Errors in Measurement.
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