I need help for a physics error analysis assignment and I have no background understanding whatsoever of statistics since I've never taken it and it all seems so foreign to me without any teaching. Can someone please help me with these questions?
1) One commonly used method is to find the "full width at half the maximum" (FWHM). To find this you determine where the number of data is one-half of the value of the maximum, i.e. where N(x) = A/2. There will be two such points for a bell shaped curve. Then the FWHM is the difference between the right hand side value and the left hand side value of x. For a Gaussian distribution what is the mathematical relationship between the FWHM and the standard deviation?
2) You have a large dataset that is normally distributed. If you choose one data point at random from the dataset, what is the probability that it will lie within one standard deviation of the mean?
Express the following quantities to the correct number of significant figures:
(a) 23.043 ± 4.321
(b) 67 ± 9.023
(c) 33.1492934 ± 2
Isn't (a) already the correct number of significant digits?
Would (b) be 67.000 ± 9.023?
Would (c) be 33.1492934 ± 2.0000000
or would
(a) 23.04 ± 4.321
(b) 67 ± 9.0
(c) 30 ± 2
A student measures three lengths a, b and c in cm and a time t in seconds:
a = 40 ± 5
b = 30 ± 3
c = 20 ± 1
t = 1.2 ± 0.1
What is a+b
a+b+c
a/t
(a+c)/t
Calculate (1.23 ± 0.03) + pi
Question 9.4. Calculate (1.23 ± 0.03) × pi
Can you do a sample calculation of each of those please?
You are determining the period of oscillation of a pendulum. One procedure would be to measure the time for 20 oscillations, t20, and repeat the measurement 5 times. Another procedure would be to measure the time for 5 oscillations, t5, and repeat the measurement 20 times. Assume, reasonably, that the error in the determination of the time for 20 oscillations is the same as the error in the determination of the time for 5 oscillations. Calculate the error in the period for both procedures to determine which will give the smallest error in the value of the period?
1 answer
1 answer