16 21 13 12 15
a) Find the mean and standard deviation (SD) of these five numbers.
b) Compare the standard deviation with its expected value, the square root of the average number.
c) Naturally, the two numbers in part b) do not agree exactly, and we would like to have some way to assess their disagreement. This problem is, in fact, one of error propagation. We have measured the number v. The expected standard deviation in this number is just Sqrt[v], a simple function of v. Thus, the uncertainty in the standard deviation can be found by error propagation. Show, in this way, that the uncertainty in the SD is 0.5. Do the numbers in part b) agree within this uncertainty?"
Opdrachten a en b zijn geen probleem. De standaard deviatie is 3,5. Opdracht c kom ik niet uit. Hoe vindt ik de onzekerheid door middel van error propagation? Wat ik deed om de onzekerheid in de standaard deviatie uit te rekenen:
\(\frac{1}{\sqrt{2(N - 1)}} = \frac{1}{\sqrt{8}} = 0,35\)
De onzekerheid in de SD is dus 0,35 * 3,5 = 1,2. Volgens de vraag moet het antwoord 0,5 zijn, maar hoe kom ik daarop?