Questions tagged [statistics]
677 questions
178
votes
21 answers
How do you make more precise instruments while only using less precise instruments?
I'm not sure where this question should go, but I think this site is as good as any.
When humankind started out, all we had was sticks and stones. Today we have electron microscopes, gigapixel cameras and atomic clocks. These instruments are many…
Vilx-
- 3,501
110
votes
5 answers
How do we know that radioactive decay rates are constant over billions of years?
A friend and I recently discussed the idea that radioactive decay rates are constant over geological times, something upon which dating methods are based.
A large number of experiments seem to have shown that decay rate is largely uninfluenced by…
Pertinax
- 1,007
67
votes
8 answers
Can 1 kilogram of radioactive material with half life of 5 years just decay in the next minute?
I wondered this since my teacher told us about half life of radioactive materials back in school. It seems intuitive to me to think this way, but I wonder if there's a deeper explanation which proves me wrong.
When many atoms are involved, half life…
uylmz
- 805
52
votes
7 answers
Are random errors necessarily Gaussian?
I have seen random errors being defined as those which average to 0 as the number of measurements goes to infinity, and that the error is equally likely to be positive or negative. This only requires a symmetric probability distribution about zero.…
Meep
- 4,167
39
votes
4 answers
Why most distribution curves are bell shaped? Is there any physical law that leads the curves to take that shape?
All the graphs shown below come from completely different fields of studies and still, they share a similar distribution pattern.
Why most distribution curves Bell Shaped? Is there any physical law that leads the curve to take that shape?
Is there…
Devansh Mittal
- 2,577
30
votes
7 answers
Least squares fit versus averaging
Suppose I want to find the spring constant of a spring from measured $F$ and $x$ data points. There are two basic ways to do this.
I could calculate the spring constant for each data point and average the results. $k = \frac{1}{N} \sum_i…
Luke Pritchett
- 7,369
28
votes
3 answers
Heisenberg's uncertainty principle for mean deviation?
The Heisenberg uncertainty principle states that
$$\sigma_x \sigma_p \ge \frac{\hbar}{2}$$
However, this is only for the standard deviation. What is the inequality if the mean deviation, defined as
$$\bar \sigma_x=\int_{-\infty}^{\infty} \lvert…
Zach466920
- 1,137
26
votes
4 answers
Does average lifetime even mean anything?
So today I was trying to derive an expression for the number of radioactive atoms remaining after a time $t$ if I began with $N_0$ atoms in total.
At first I tried to assume that they had an average lifetime and work from there, but my friend…
QCD_IS_GOOD
- 7,145
25
votes
9 answers
Why does a collection of radioactive atoms show predictable behaviour while a single one is highly random?
Well, we know that it is impossible to say exactly when a radioactive atom will go on decay. It is a random process. My question is why then a collection of them decays in a predictable nature (exponential decay)? Does the randomness disappear when…
Sabbir Ahmed
- 567
25
votes
5 answers
Why do coherent states have Poisson number distribution?
In quantum mechanics, a coherent state of a quantum harmonic oscillator (QHO) is an eigenstate of the lowering operator. Expanding in the number basis, we find that the number of photons in a coherent state follows a Poisson distribution.
Is there…
knzhou
- 107,105
24
votes
3 answers
How to combine measurement error with statistic error
We have to measure a period of an oscillation. We are to take the time it takes for 50 oscillations multiple times.
I know that I will have a $\Delta t = 0.1 \, \mathrm s$ because of my reaction time. If I now measure, say 40, 41 and 39 seconds in…
Martin Ueding
- 8,559
24
votes
3 answers
How do you find the uncertainty of a weighted average?
The following is taken from a practice GRE question:
Two experimental techniques determine the
mass of an object to be $11\pm 1\, \mathrm{kg}$ and $10\pm 2\, \mathrm{kg}$.
These two measurements can be combined to
give a weighted average.…
Jonathan Gleason
- 8,834
21
votes
7 answers
Line of Best Fit with or Without Constant Term
Some other physics teachers and I were discussing an AP problem about a potential experiment for measuring $g$ and disagreed on the best way to use a line of best fit to analyze the data.
The experiment measures the acceleration of an Atwood machine…
Luke Pritchett
- 7,369
20
votes
2 answers
How do we know that some radioactive materials have a half life of millions or even billions of years?
If a radioactive material takes a very long time to decay, how is its half life measured or calculated? Do we have to actually observe the radioactive material for a very long time to extrapolate its half life?
davitenio
- 303
19
votes
4 answers
Factor 2 in Heisenberg Uncertainty Principle: Which formula is correct?
Some websites and textbooks refer to $$\Delta x \Delta p \geq \frac{\hbar}{2}$$ as the correct formula for the uncertainty principle whereas other sources use the formula $$\Delta x \Delta p \geq \hbar.$$
Question: Which one is correct and why?
The…
Patrick
- 291