Question

only one problem (Exercise 1-11 only)

Uncertainties in Measurement and Propagation of Errors one measurement is made and often the peecision of the instrument is used as arn mate of the uncertainty. the instrument and the situation, the uncertainty Depending upon could be less than the precision of the instrument or it could be more. For example, in measuring we may estimate the distance between the small est subdivision (mm) if we rurn the meter stick onto its side to eliminate parallax. Therefore, the uncertainty in the measurement mighe be 05 mm or even 0.3 mm rather than the precision of the mete stick which is 1 mm. On the other hand, if we measure an objece that is not right next to the meter stick, the uncertainty might be 2 or 3 mm. Often İudgment is required in order to estimate the uncertainty in a single measurement We shall employ the same symbol, d,, to denote estimated uncertainty in this manual Reporting Uncertainties The uncertainty in an experimental quanticy muse be reported. Since there are a number of ways to do this we must state the meaning of theuncertainty. A common method is to report x ± σ together with the number of measurements n. The reader can quickly calculate d In the remain- der of this manual, we shall either quote the standard deviation or the estimated uncertainty as the uncertainty Table 1-2. Weight of a Bea ws- 1.96 x 10 -194x 30 W- 2.03 X 10 W-198 x 10 1.96 × 10 4 Wa-2.00 x 10 W 197 x 10 10 we-L95 × 10-4 Wu-2.00 10.4 wha= 1.97 × 10. W- 1.99x 10 12 Example 1-5. To illustrate these ideas, we might measure the weight of a lea twelve times with a balance of precision 0.01 X 10-*N. The results are tabulated in Table 1-2. The mean wecight, according to eq I1, is: = 1.96+1.94+ +197× 10" N Note that we have retained one more significant figure for W. for the purpose of cakculating (1.96-1.980)'++1.97-1.980)x 10N 12 = 1.980× 10" N. the sample standard deviation, which is 12-I 0.02662874 × 10" N

Answer 1

Mean and standard deviation of a frequency distribution table of number of heads in tosses of 10 pennies

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