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. H

    Need help with arduino sampling voltage and current

    Hi, I built a electrolytic cell that uses electricity to break water into hydrogen and oxygen. I am testing efficiency and need a way of calculating the average current draw and voltage drop over a period of time for the cell. I have some experience using Arduinos in projects but not much. I...
  2. jegues

    What is the Minimum Sampling Frequency for a Sinusoidal Signal?

    Homework Statement See figure attached. Homework Equations The Attempt at a Solution I'm quite sure what he's getting at with this problem... The minimum sampling frequency would be 2 times the maximum frequency component of the signal. Since this is a sinusoidal signal, it...
  3. DrChinese

    Fair Sampling Loophole now closed for Photons

    A team including Anton Zeilinger has performed an experiment closing the so-called "fair sampling loophole" for photons. http://arxiv.org/abs/1212.0533 Bell violation with entangled photons, free of the fair-sampling assumption Marissa Giustina, Alexandra Mech, Sven Ramelow, Bernhard...
  4. R

    Inference on original population based on sample - estimating sampling probability

    In my research I am working on some data (let’s call it sales data), however we almost have no information on the original sample. My goal is to come up with possible explanations on how it could be sampled by consistency arguments. In more detail, the data provided is composed of sales...
  5. F

    Square wave, sampling and verilog clocks

    Homework Statement Homework Equations My question too :) The Attempt at a Solution Can anybody confirm whether I solved the problem right or wrong? As for the next question about verilog and many clocks I am unable to find a source with that information. Thanks a lot for any...
  6. R

    HELP WITH STATS - Good sampling methods for this would be what?

    URGENT HELP WITH STATS - Good sampling methods for this would be what? Are the ones I selected right? I only get one submission. Please please help!
  7. S

    MHB Help with this double sampling scheme problem

    Please help with a hint of doing his question, I have drawn the diagram but still confused. Q)In a food production process, packaged items are sampled as they come off a production line. A random sample of 5 items from each large production batch is checked to see whether each item is...
  8. C

    Point estimate from multiple sampling distributions

    Dear all, I hope someone can help me. I have two experimental groups, A (n=5) and B (n=8) containing biological samples. The samples are used to estimate my parameter of interest, θ. I do this with Markov-chain Monte-Carlo, which gives me a posterior distribution of θ for each of my samples...
  9. M

    MHB Estimating a Population from Sampling with Imperfect Detection

    Hello All, thanks for looking at my post and question. I have jumped into deep statistical and probability waters which have outstripped my current state of knowledge so any help you can render would be greatly appreciated. Here is my question: I am trying to get an estimate of the original...
  10. E

    Quantile function for leptokurtotic sampling distribution

    I have a research problem that requires me to find the 95th percentile of a sampling distribution like this: http://www.nuclearphynance.com/User%20Files/9231/1minVARCLOSE.png My first question is, what would be a mathematically sound way to calculate something like this, with several clusters...
  11. A

    Sampling Error, Homogenous Mixture, Heterogenous Mixture: Benefits/Drawbacks

    Why do you have to use a homogenous mixture in an experiment what are the disadvantages of using a heterogenous mixture?
  12. C

    Signal Processing: Up and Down Sampling

    Homework Statement Does the upsampling and downsampling have any effect on the amplitude? consider the following X(e^jw) Homework Equations what will be the amplitude of the signals? do they remain 1 or are they to be divided/multiplied by L/M, L being upsampling factor and M...
  13. T

    Periodicty - Sampling of a periodic signal

    periodicty -- Sampling of a periodic signal... I have a doubt..is a signal which is sampled from a periodic signal also periodic?if so then is there a relation beyween the time period of the two?
  14. S

    Computability meets Random Sampling

    Some things are physically impossible, but mathematically possible (like exactly bisecting a line segment). Some things are both physically and mathematically impossible (like exactly trisecting an angle "with a ruler and compass".) Things mathematically impossible are proven to be so...
  15. D

    Sampling frequency and square waves

    Homework Statement Lets say I have a square wave of 10Hz. I want a good sampling frequency or the Nyquist rate (minimum) to accurately capture its characteristics without aliasing. Is it enough to use 10Hz x 2 as nyquist rate, or must I break it down into harmonic frequencies? and use...
  16. T

    Strangely Small Sampling rates with a 400 MHz Oscilloscope

    I'm doing an experiment using a super fancy oscilloscope. I'm measuring a tiny output voltage that varies with time. I was instructed to make my sampling rate as small as possible (~500S/s). Now the signal that I'm looking at is, in other applications when its being sent to a computer and...
  17. G

    Nyquist sampling rate and signal anti-aliasing

    Hi all! Quick question. If a Nyquist sampling rate in a signal is 2f, what lower frequencies can be represented without aliasing? I assume you could have frequencies which have only even number of samples in their wave length, or maybe in half of their wave length. Am I wrong? If someone can...
  18. M

    MHB Can t-tests be used to compare ecological indices from different sampling sizes?

    Hello everyone I would like that you may help me with this following question: I have data from plant species occurrences from 30 sites (10 beaches with 3 replications for each one; 6 beaches not in erosive process; 4 in erosive process) in coastal dunes vegetation. At each site I have made...
  19. B

    How to obtain the sampling frequency of frequency data

    Hi everybody, this is my first question in this forums. I have some complex data in Matlab the absolute value of which represent a frequency response. My data extend from 1 Hz to 20 kHz and have an incremental frequency of 1 Hz. I now need to convert this frequency responses in Impulse...
  20. I

    Mathematica Efficient sampling of function. [Mathematica]

    Hey there PF. I wanted to ask here if someone had any input as to why a tiny part of my code is "slow". I have sloved a somewhat big eq.system numerically with Mathematica. Now, I do not really need the actual integrated functions and so I sample them. Below: I sample (picks out only 4...
  21. F

    Calculating Minimum Sampling Rate for Fourier Signal

    Hello, I have the following Fourier complex signal: v(t) = 2/πsin(500πt)+1/2sin(1000πt)+1/3sin(1500πt) I need to find the minimum sampling rate for this signal. So, according to the Nyquist Theorem, the sampling rate must be twice the highest frequency component contained in the original...
  22. F

    Quadrature sampling detector circuit

    Hi. I'm trying to build a quadrature sampling detector, or Tayloe detector based on the design at http://garage-shoppe.com/wordpress/?p=371 . I intend to feed the I and Q signals into a ADC that uses a 1.65V reference. One thing I'm confused about is the purpose of the 2.5 VDC offset fed into...
  23. E

    Sampling distribution of mean item number?

    Homework Statement If you have a box of 1,000 items, with numbers 1-10 on them, 100 for each! And this proves the discrete uniform probability distribution. 1/10 for each.Homework Equations Mean = u = Exp(x) = e(x) St dev worked out by the variation. St Dev = square root of the variation...
  24. N

    Sample Size and Standard Deviation of the Sampling Distribution of the Mean

    Hi, I am doing an undergraduate introductory statistics course and I'm trying to understand some basic concepts. I'm trying to understand why the sample size (n) affects the standard deviation of the sampling distribution of the mean (σ_{M}) I understand how a sample size affects the...
  25. B

    Nyquist Sampling Theorem - I just understand this.

    Hello! I am having a difficult time understanding the "Nyquist Sampling Theorem." I was wondering if someone can help me understand this. Below is an example out of my book: Q: Suppose that an analog signal is given as x(t) = 5cos(2*pi*1000t), for t > 0 and is sampled at the rate...
  26. A

    Question about sampling size.

    My experience with statistics is very limited although I understand probability theory quite well. My friend, an accountant, asked a question. He does attribute sampling. I understand most of it intuitively and the math was what I expected it to look like when I got curious and started reading...
  27. M

    Random Sampling: Set Inclusion

    Hello, I don't really know if this is considered a challenging problem but this is not for homework: You're given a set of numbers S of size n. From S, you draw a random sample A, |A| < n. From S, you draw a random sample B, |B| < n. Sampling doesn't remove items from S. What is the...
  28. A

    Need help from someone who knows about importance sampling.

    Hello! My question is about Importance Sampling. I am trying to apply a complex sampling method, which combine two sampling techniques. To do this, the importance sampling is used ONLY to divide the probability distribution into two main parts: Part 1: from 0 to p*, and Part 2: from p* to 1...
  29. M

    How does Excel anticipate a sampling distribution using just one sample?

    Hi, I know that Standard Error of a coefficient is the standard deviation of the sampling distribution associated with the coefficient. I understand the concept. What puzzles me is this: We have just one random sample to work with. The calculator or Excel doesn’t have any info on the...
  30. A

    What type of sampling is this?

    Hi, I hope you can help. I collected my samples on the street by just asking passers by to fill in my questionnaire. I moved to 5 different locations within the city and spent 3 hours each visit 3 times a week for one month. Is this random sampling? Or it it sill convenience sampling? Can...
  31. B

    Why is 44100 Hz the standard sampling rate for compact discs?

    I know that from the sampling theorem you have to go at least twice the frequency you want to sample. Human hearing is around 20 kHz. So 40 kHz would be enough. What are those extra 4100 Hz there for. Now don't get me wrong, I tried google but all results were vague and only scratched the...
  32. C

    How to use monte carlo method : importance sampling ?

    Hello.I have a little problem with applying a Monte Carlo method : Importance Sampling.I need to calculate : integral(0 to infinity) integral(0 to infinity) 1/(2 * pi * sqrt((1 + x^2 + y^2)^3))dxdy Can somebody help me ? Thanks in advance.
  33. F

    Down sampling, bandpass sampling theorem, downconversion

    I'm trying to demodulate simple AM by using an ADC and the bandpass sampling theorem (as I understand it.) The way I understand the theorem is that by sampling a bandpass signal of frequency f_{0} and bandwidth B, where f_{0} >> B, as long as I use a sampling frequency of >2B I can reproduce...
  34. B

    MATLAB 44100 Hz signal sampling, matlab question

    So I was playing in MATLAB with signals. I recorded myself saying some sample sentence. I imported it as a vector (it was mono), and reproduced it and it worked. But then I told matlab, to skip every other element. Basically I wrote this: soundsc(a(1:2:end),44100). what I EXPECTED was to...
  35. F

    Nyquist Sampling Rate Question

    They say you can fully recover a signal if you sample it at twice the bandwidth (Nyquist rate). But how is it possible to be able to fully recover the signal since you are missing all the information about the signal between successive samples? For example if you sample cos(2*pi*B*t) at 2B...
  36. J

    Nyquist - shannon sampling theorem example

    Homework Statement What sampling frequency would you use to sample the following signal x(t) = 3sin(9πt) - 6cos(8πt)Homework EquationsThe Attempt at a Solution let T1 be the period of 3sin(9πt) and T2 the period of 6cos(8πt) T1 = 2π/9π = 2/9 Τ2 = 2π/8π = 2/8 thus, if f1 is the frequency of...
  37. B

    Solving Sampling with Aliasing Homework

    Homework Statement Let the signal x(t) = \left(\displaystyle\frac{\sin(50\pi t)}{\pi t}\right)^2, which we want to sample with sampling frequency \omega_s = 150\pi in order to obtain a signal, g(t) whose Fourier transform is G(\omega). Determine the maximun value for \omega_0 which guarantees...
  38. F

    Sampling distribution of a difference between two independent sample proportions

    My apologies that this doesn't fit the template. Example 10-3 on...
  39. M

    Sampling of a gaussian distribution

    I have a 3d data cube. For every point I measure the property A which is a gaussian variable of mean m and variance s and it's also a function of the density d at every point. A(x,y,z)=f(d(x,y,z))e^(-(X-m)^2/(2\sigma^2)) X is a random number. Now let's say I want to sample the...
  40. L

    Recovering a Signal Under Nyquist Sampling Constraints

    Homework Statement A signal x(t) with Fourier transform X(jw) undergoes impulse-train sampling to generate xp(t) = sum[ x(nT)deltafnc(t-nT) Where T = 10^(-4), Determine with these constraints whether the signal can be recovered. a) X(jw) = 0 for |w|> 5000pi Homework Equations...
  41. T

    Bit rate, symbol rate and sampling in LTE

    Hi guys, I have a problem in understanding LTE. LTE is the long term evolution 4G technology. The LTE requirement is 100 Mbps with 1.3, 2.5, 5, 10, 15 and 20 MHz for 128, 256, 512, 1024, 1536 and 2048 subcarriers. Each bandwidth corresponds to each number of subcarriers. My problem here...
  42. G

    What are audio sampling signals?

    Does anyone know what audio sampling signals? Not Audio sampling but Audio sampling signals Thanks.
  43. G

    What are audio sampling signals and what is the required minimum sampling rate?

    Hi, I have a question and I was wondering whether you might help me, because I have done a lot of research nut no clues. Just bits and pieces. Thanks ALOT Homework Statement In digital transmission, what are audio sampling signals? What is the mimimum sampling rate required...
  44. M

    Combine several measures: consensus mean or a sampling problem?

    Combine several measures: "consensus mean" or a sampling problem? Dear all, I have this problem: the work aims to test the value (mean and error) of several sensors (with a different measure for each) in a subjects group, and then to have a single global value (a single mean and error) from...
  45. M

    Attenuated system with unknown sampling rate

    A causal system is composed of the series cascade of two LTI subsystems with impulse responses (1/2)nu(n) and (1/3)nu(n-1). A tone at 1 kHz is attenuated by 43.6%. Can you tell what the sampling rate is? My thought process.. I have only solved problems where I had to find the attenuation...
  46. S

    Increasing variance of weights in sequential importance sampling

    Hi all, I know about these facts: 1- The variance of importance weights increases in SIR (also know as the degeneracy problem). 2- It's bad (lol), because in practice, there will be a particle with high normalized weight and many particles with insignificant (normalized) weights. But I...
  47. C

    Sampling and recovering a Sawtooth wave

    Hey guys, I've been working extensively on a report for the last few hours. I've managed 28 pages but I'm stuck on something. For a 33kHz sampling of a sawtooth wave, what would the recovered wave look like? I'd imagine it would be recovered through a low pass filter? Also, why is the wave...
  48. D

    FFT minimum sampling duration

    I am wondering what the minimum sampling duration must be in order to accurately resolve a 60Hz wave. I know the FFT works with periodic waves about the number N but I am not sure how this relates to say a sampling duration that is 1 half the sampling period of a 60 Hz wave. I'm worried that the...
  49. A

    What type of sampling is this `

    What type of sampling is this...` I want to distrubute questionaires to five groups of people with different educational back grounds; • Group 1; No GCSE’s • Group 2; Some GCSE’s • Group 3; Higher education (A-levels, college course, NVQ etc) • Group 4; University Graduates • Group 5...
  50. L

    Estimator for variance when sampling without replacement

    Does anyone know the formula for an unbiased estimator of the population variance \frac{1}{n}\sum_{i=1}^{n}(x_i - \bar{x})^2 when taking r samples without replacement from a finite population \{x_1, \dots, x_n\} whose mean is \bar{x}? A google search doesn't find anything useful other than the...
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