# What is Sampling: Definition and 207 Discussions

In statistics, quality assurance, and survey methodology, sampling is the selection of a subset (a statistical sample) of individuals from within a statistical population to estimate characteristics of the whole population. Statisticians attempt for the samples to represent the population in question. Two advantages of sampling are lower cost and faster data collection than measuring the entire population.
Each observation measures one or more properties (such as weight, location, colour) of observable bodies distinguished as independent objects or individuals. In survey sampling, weights can be applied to the data to adjust for the sample design, particularly in stratified sampling. Results from probability theory and statistical theory are employed to guide the practice. In business and medical research, sampling is widely used for gathering information about a population. Acceptance sampling is used to determine if a production lot of material meets the governing specifications.

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1. ### I Sampling theory and random sample

In inferential statistics, we have a large population, collect data from it to get random sample of size ##n##, and infer the population parameters from that single sample. I read that the random sample can be interpreted as the collection of the ##n## realizations of a single random variable...
2. ### Which Circuit is Best for Sampling Voltage and Current in the 250V, 30A Range?

Hello, Please help me to create the sampling processing circuit. i have to create the voltage and current sampling processing circuit, Then the output of circuit will be fed to processor to further operation. output voltage of my original circuit will be maximum 250v and current is 30A(peak...
3. ### I What is a distinct feature of an ambiguous result?

This question comes from my experience in radar signal processing. As I am going more deep into the theory of sampling, statistical signal processing and estimation theory in general, I have a very silly but important mathematical question that I want to ask here. For example, we are estimating...
4. ### I Martingale, Optional sampling theorem

In this exercise, we consider simple, nonsymmetric random walk. Suppose 1/2 < q < 1 and ##X_1, X_2, \dots## are independent random variables with ##\mathbb{P}\{X_j = 1\} = 1 − \mathbb{P}\{X_j = −1\} = q.## Let ##S_0 = 0## and ##S_n = X_1 +\dots +X_n.## Let ##F_n## denote the information...
5. ### Music Identify this old film sampling in this song

I really like this song by Hudson and Troop called Against the Grain, but it's driving me crazy. Here it is on Spotify. It seems to sample what sounds a whole lot to me like a Sci-fi Disney show from the 70s - you know, like The Computer Wore Tennis Shoes kind of thing. But try as I might, I...
6. ### A The expectation of the sampling distribution of Pearson's correlation

The shape of the sampling distribution of the Pearson product moment correlation coefficient depends on the size of the sample. Is the expectation of the sampling distribution of the Pearson product moment correlation coefficient always equal to the population correlation coefficient, regardless...
7. ### A Sampling Electrons from a 2D Projection: Is There a Functional Form?

Hello! I have some electrons produced from a 3D gaussian source isotropically inside a uniform electric field. The electric field guides them towards a position sensitive detector and I end up with an image like the one below (with more electrons on the edge and fewer as you move towards the...
8. ### I Bell's circuit beginner's question: Sampling alters, - what's normal?

Yes, I should hit the books more, so forgive the basic question. I take it normality is known by observing unsplit photon spin ? But how can one then exclude that split photons in themselves might have different probability outcomes ? Thx much in advance. (Please pardon that only...
9. ### Sound card sampling rate 1.2msps?

I am designing an experiment for pam-ook which acquires a radio audio signal to the mic input of my laptop. I process the signal using c++ code employing an audio library (PortAudio) which provides the data stream. I require a sampling rate of 1.2msps but the sound card in my laptop has a...
10. ### Model Fuel Assembly w/ Gamma Source: Solving a Sampling Problem

Hi everyone, I'm making a fuel assembly model and I would like to have a cylindrical gamma source on each fuel rod to measure the decay heat of a fuel assembly but I'm struggling to define the source since it is in a repeated structure. This is the geometry of my model: Level 2 : cells 1, 2 3...
11. ### A How to derive the sampling distribution of some statistics

Assume that ##T## has an Erlang distribution: $$\displaystyle f \left(t \, | \, k \right)=\frac{\lambda ^{k }~t ^{k -1}~e^{-\lambda ~t }}{\left(k -1\right)!}$$ and ##K## has a geometric distribution $$\displaystyle P \left( K=k \right) \, = \, \left( 1-p \right) ^{k-1}p$$ Then the compound...
12. ### MHB Sampling Distribution of the Sample Means from an Infinite Population

1. Individual students’ scores on a national test have a normal distribution with a mean of 18.5 and a standard deviation of 7.8. At a Trade School, 84 students took the test. If the scores at this school have the same distribution as national scores, what is the mean, standard deviation and...
13. ### Rigorous mathematical definition of sampling

Please could you help me find a rigorous mathematical definition of sampling as it is used in mathematical statistics? Let ##X:\Omega\rightarrow\mathbb{R}## be a random variable and ##X_{1},...,X_{n}## is a statistical sample. What is its mathematical meaning in probability theory? Are we...
14. ### Effective way of slurry sampling

I have ~50% slurry mass in a reactor with (4 PBT + 4PBT) agitator. Agitator is rotating at 94 RPM. To analyze reaction mass we are sending two samples at a time from bottom of the reactor. There is significant analysis deviations in these two samples. I feel that the sample is not...

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16. ### Digital Filters: why is sampling frequency equal to 2*pi unit circle

Hi, I was working through a filter design problem and got stuck on a concept. Scenario: Let us say we have the following pulse transfer function and the sampling frequency is ## f_s = 50 \text{Hz} ##. G(z) = \frac{1}{3} \left( 1 + z^{-1} + z^{-2} \right) The zeros of the transfer function...
17. ### MHB This is sampling distribution can you help me with this problem

1. The weight of goats at a farm is normally distributed with a mean of 60 kg and a standard deviation of 10 kg. A truck used to transport goats can only accommodate not more than 650 kg. If 10 goats are selected at random from the population, what is the probability that the total weight...
18. ### Optimal Discrete Sampling of Histogram

I am wondering if this problem has a name, and what is the most efficient way to solve it. Say you have a normalized histogram ##h(P)## (representing a pdf estimated from a large population), with ##n## bins, you want to generate a sample of points ##S## from ##h(P)## of size ##k##, such that...
19. ### I Stratified sampling based on properties of random number streams

I recall seeing briefing notes dating from about the 1970's that advocated doing stratified sampling of the outputs of simulations by using strata based on properties of the random number streams. However, I don't recall how the strata were to be defined. Is this type of stratified sampling a...
20. ### MHB How Can a Random Number Table Be Used to Sample Cotton-Top Tamarins?

okay guys this is the question: A zoo has 80 cotton-top tamarins. Describe in detail how the random- number table given below could be used to select a sample of 5 of them, for a study of tail lengths. 8330 3992 1840 0330 1290 3237 9165 4815 0766 (5marks) So I am not really sure where to go...
21. ### I Estimating Gene Mutation Proportion: A & B Approaches

The proportion of individuals that carry a certain gene mutation in the population is unknown. A research assistant at a medical laboratory wants to estimate this proportion. The research assistant is thinking of two approaches: A. Take blood samples from all individuals that come to the...
22. ### MATLAB Deconvolving two signals with different sampling rates

Hi, So i am in a fix now. I have a discrete time signal which is produced by a device with Nyquist frequency as 50MHz and 1088 samples (there is nothing i can do with the device to change the frequency or number of samples). I have an analytical signal which is produced in the frequency domain...
23. ### Instrument name for water sampling and analysis

Hello, thank you for your attention in my thread. I'm the head of Youth Science Club on one of the many High School in Indonesia, I got many members and I want to guide them for doing water sampling and analysis. In the history of my high school, no one is able to do water sampling and...
24. ### Find the sampling matrix and sampling structure for R, G and B components

Hello, everyone. :) All I could gather is that, if I'm correct, lattices are spans of the column vectors of the matrix within the "LAT()" notation and the X and Y occurrences are unit placeholders (such as the pixel unit (since this is in the context of image processing)). And, as an attempt...
25. ### How to solve this sound problem (minimum sampling rate required)

Summary: The problem: If one wants to make a digital record of sound such that no audible information is lost, what is the longest interval, Δt, between samples that could be used? ( it gives a hint that humans can hear sound waves in the frequency range 20 Hz to 20 kHz. It should be a very...
26. ### Sampling distribution's magnitude variation

I have generated a distribution (normalized such that the sum is equal to 1) by using the code: M=500; % Number of samples z=1; SUM = 1; ns = rand(1,M).^z; % random numbers TOT = sum(ns); X = (ns/TOT)*SUM; % Re-scaling hist(X(1,:),100) For an exponent ##z=1##, the sampling distribution is...
27. ### I Stratified Random Sampling vs Simple Random Sampling

I'm beginning to learn statistics and I quite didn't understand the formula for the stratified random sampling. Let's say we have a country with 3000 people, divided into 3 cities containing 1000 people. We want to know the proportion of women in the whole country so we decide to take a sample...
28. ### Does the Nyquist Sampling Theorem Apply to Square Waves?

Homework Statement In comparison with the sampling sine wave, in order to reconstruct a square wave, do we need to increase or decrease sampling frequency? Homework Equations Aliasing effect Leakage effect The Attempt at a Solution No matter square wave or sine wave, the experimental results...
29. ### I Anyone familiar with Compressive Sensing (sampling)?

Hello Everyone, Is anyone familiar with the technique of compressive sampling? I am trying to grasp how it works, its strengths, etc. It is a way to decompose signal and reconstruct them from fewer information than the traditional transforms (Fourier, etc.) or compressive algorithms... Thanks!
30. ### A Inverse function of the Nyquist-Shannon sampling theorem

I'm currently carrying out an analysis on waveforms produced by a particular particle detector. The Nyquist-Shannon sampling theorem has been very useful for making an interpolation over the original sample points obtained from the oscilloscope. The theorem (for a finite set of samples) is given...
31. ### I Local Sampling vs Global Sampling

So from what I understand from my readings in Shankar's QM book, in the preface, that Newton's Laws give a particle some local sampling of the gravitational field around it and then decides where to move next based on the current step and that the sequential sum of all the path segments(...
32. ### Basic Sampling Question: Understanding Frequency Change in Piecewise Sinusoid

Homework Statement Hi, I have the following continuous sinusoid given by Now, if I sample this with a sampling rate of $$f_s = 4f_0$$ , I am told this is the answer, I don't understand that. How come the frequency of the sinusoid has changed? I already studied sampling, etc. but this...
33. ### I Sampling Weights: Understanding Multipliers & Aggregates

Hi, I am trying to understand weights or multipliers allocated to sample in my data(for my research work). They have given a formula as how weight is calculated and how aggregates are to be obtained. But what I am trying to understand is how they obtained the formula for multiplier which they...
34. ### I Sampling from a multivariate Gaussian distribution

I was watching a lecture on youtube about linear regression and there's a section where it had the statement below (written in purple). Does multiplying by sigma rotate the distribution to make it look like x - N(mew, sigma^2)? Mew in this case is 0 so it doesn't shift the distribution.
35. ### Sampling Distribution Question

I've added a screenshot (https://imgur.com/a/isQXZ) and the text below for your convenience. Please show steps if possible to help my understanding. Thank you. Consider a random variable that is Normally distributed, with population mean mu = E [X] and population variance sigma^2 = var [X]...
36. ### Help interpreting a design for power management unit

Hello, I have been looking to build a pmu similar to this device, it will be for domestic use. https://www.digikey.com/en/articles/techzone/2014/jan/low-cost-microcontroller-based-phasor-measurement-units-improve-smart-grid-reliability I am having a bit of trouble with the sampling part and...
37. ### How to Measure Biomass Yield in a Non-Homogeneous Anammox Bioreactor?

We have in our lab a continuous anammox bioreactor, however, it is not well mixed, i.e. all the biomass is concentrated at the bottom of the reactor. We're interested in quantifying the biomass yield. Does anybody know of any techniques to measure this in a continuous non-homogeneous bioreactor...
38. ### How to choose the sampling time for the delay unit

hi, i am designing a fuzzy logic controller, i need to use a delay block for the change in error signal now i don't know that based on what factors should i choose the sampling time for this unit
39. ### Is Nyquist Theorem Applicable to a Detector with 500 Pixels and 5um Pixel Size?

Homework Statement Given a detector with 500 pixels, and a pixel size of 5 um, is it posible to register next signal? I = cos(2 π 4 x) were x is expressen in umHomework Equations fs = fs/2 The Attempt at a Solution My problem is with the pixel size, I mean, the sampling rate will be...
40. ### MHB Is the sampling distribution for skewness and kurtosis normal?

The Central Limit Theorem specifically calls out a sample mean to be following normal distribution (for n>=30 ), But I am referring to certain text, and it is calculating z values for sample skewness and sample kurtosis assuming that these follow Normal distribution. Is it correct? In short...
41. ### Does anybody know the sampling frequency of a cop radar?

More specifically, does anybody know the sampling frequency of a mounted 360 degree cop radar? NOT a conical/directional hand-held radar gun.
42. ### I Sampling and analysis of variance

Dear forumers, In advance, thank you for reading this post and helping me solving this. The problem is the following : I have a population (say, a bag) from which i take 3 samples. Each sample gets analysed once by a laboratory in order to know their concentration of a product. The result...
43. ### Sampling a continuous-time signal, aliasing/Nyquist

Homework Statement The analog signal x(t) = cos(2pi f t) is sampled at a rate of 1 kHz, using ideal impulse sampling, to obtain the sampled signal x^(s)(t). The sampled signal is then sent through an ideal lowpass filter with transfer function H(2pi f ) = 0.001 rect (0.001 f ). (a) If f...
44. ### Optimal Sampling Rate for Spectrum Replication: Expert Homework Help

Homework Statement In some cases, the spectrum replication property of sampling can be used as a substitute for demodulation. Given a signal xa(t) with the spectrum shown, what is the lowest sampling rate that will ensure both no aliasing of the spectrum, and that one of the spectrum replicas...
45. ### Sampling an ac waveform on microcontroller

I did a small project on ac power measurement using arduino a few months ago. But it was specifically for 50Hz supply only. I sampled the waveform in a 20ms interval and applied DFT to get the amplitude and phase. This works good when the frequency is between 49.5 Hz to 50.5 Hz. The aim was to...
46. ### MHB Stratified Sampling: Sample Size from Greslow High

There are three secondary schools in Banley. The table shows the number of students in each of these schools. Adis College_Greslow High_Fripp School 750 700 900 Germaine takes a sample of 50 students stratified by school. Work out the number of students from...
47. ### A Using Metropolis-Hastings for Sampling from a CDF

Hi If I have a CDF = integral wrt t from 0 to r^2/2 of 2*sqrt(pi*t)*e^(-t)*dt but I want to generate samples from the PDF, would Metropolis-Hastings algorithm be the best alternative? Rgds rabbed
48. ### What Frequencies Emerge in a Sampled Signal of Mixed Sine Waves?

Homework Statement A continuous signal $$x(t)=15\sin (10t)+5\sin(30t)+3\sin(50t)$$ is sampled with frequency $\Omega =4.0$ Hz. Which frequencies are present in the sampled signal? Homework EquationsThe Attempt at a Solution No idea really. I seriously doubt it is that easy: Frequencies...
49. ### Problems regarding signal sampling

Homework Statement I have created four signals in Matlab and we need to play the sound of these signals. The four signals I've created are: n=[0:8191]; w0=2*pi*2000; T=1/8192; t=[0,1]; t=n*T; x=sin(w0*t); sound(x,1/T); ----------------- n=[0:8192]; w0=2*pi*2000; T=1/8192; t=[0,1]; t=n*T...
50. ### Demon algorithm for microcanonical ensemble

I simulated a microcanonical ensemble of 10 ideal gas particles in one dimension and yielded the expected normal distribution of velocities. However, I still did not get how the algorithm works. The demon has non-negative energy content and the demon together with the system constitutes a closed...