What is Stats: Definition and 248 Discussions

Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data. In applying statistics to a scientific, industrial, or social problem, it is conventional to begin with a statistical population or a statistical model to be studied. Populations can be diverse groups of people or objects such as "all people living in a country" or "every atom composing a crystal". Statistics deals with every aspect of data, including the planning of data collection in terms of the design of surveys and experiments.When census data cannot be collected, statisticians collect data by developing specific experiment designs and survey samples. Representative sampling assures that inferences and conclusions can reasonably extend from the sample to the population as a whole. An experimental study involves taking measurements of the system under study, manipulating the system, and then taking additional measurements using the same procedure to determine if the manipulation has modified the values of the measurements. In contrast, an observational study does not involve experimental manipulation.
Two main statistical methods are used in data analysis: descriptive statistics, which summarize data from a sample using indexes such as the mean or standard deviation, and inferential statistics, which draw conclusions from data that are subject to random variation (e.g., observational errors, sampling variation). Descriptive statistics are most often concerned with two sets of properties of a distribution (sample or population): central tendency (or location) seeks to characterize the distribution's central or typical value, while dispersion (or variability) characterizes the extent to which members of the distribution depart from its center and each other. Inferences on mathematical statistics are made under the framework of probability theory, which deals with the analysis of random phenomena.
A standard statistical procedure involves the collection of data leading to test of the relationship between two statistical data sets, or a data set and synthetic data drawn from an idealized model. A hypothesis is proposed for the statistical relationship between the two data sets, and this is compared as an alternative to an idealized null hypothesis of no relationship between two data sets. Rejecting or disproving the null hypothesis is done using statistical tests that quantify the sense in which the null can be proven false, given the data that are used in the test. Working from a null hypothesis, two basic forms of error are recognized: Type I errors (null hypothesis is falsely rejected giving a "false positive") and Type II errors (null hypothesis fails to be rejected and an actual relationship between populations is missed giving a "false negative"). Multiple problems have come to be associated with this framework, ranging from obtaining a sufficient sample size to specifying an adequate null hypothesis. Measurement processes that generate statistical data are also subject to error. Many of these errors are classified as random (noise) or systematic (bias), but other types of errors (e.g., blunder, such as when an analyst reports incorrect units) can also occur. The presence of missing data or censoring may result in biased estimates and specific techniques have been developed to address these problems.

View More On Wikipedia.org
  1. Steve Zissou

    I Relating Moments from one Distribution to the Moments of Another

    Ok, I'm sure I can find a smarter way to pose this question, and I will try to define the question more carefully in coming days. That having been said, consider this: Let's say we have a random variable X (or whatever). I can calculate the moments of this variable with no problem. In fact let's...
  2. ForTheLoveOfPhysics

    B Data needed - Related bodies and their stats

    I’m analysing the gravitational relationships between different mass astronomical bodies and am getting sick of having to individually google and document these. Are there data sets out there that list pairs/sets of objects which includes their mass and distance from each other? Including...
  3. jim mcnamara

    US Covid Deaths Reaching 1M: 997041 in 2022/18/03 18:51 MDT

    Per Worldometer 2022/18/03 18:51 MDT data: Reported Covid US deaths 997041, World deaths 6093047 Population of the US 334256039, World (est) 7934365211 USA as % of world population 4.2% USA as % of world Covid deaths 16.3% In a short while the Worldometer counter for USA deaths will hit 1...
  4. K

    Quantum Finding the Perfect Self-Study Book for Intro Stats & Quantum Mechanics

    Can you please suggest a good introductory statistical and quantum mechanics book which can be self studied. My math background : I've done multivariate calculus, vector calculus, linear algebra ,some complex analysis all at the usual undergraduate level. The books I've self studied thus far...
  5. M

    I Bayesian Stats: Resources about Mercer's Theorem for Gaussian Processes

    Hi, Question(s): 1. Are there any good resources that explain, at a very simple level, how Mercer's theorem is related to valid covariance functions for gaussian processes? (or would anyone be willing to explain it?) 2. What is the intuition behind this condition for valid covariance...
  6. G

    Physics What kind of graduate schools should I apply to given my stats?

    Hello, I am a senior physics student who is interested in applying to graduate school for physics. I am having a hard time figuring out where to apply, what my safe, match and reach schools are, and in general deciding where I can even get into if I apply so I don't waste hundreds of dollars on...
  7. P

    B Stats: Determining significance level in problem

    Question: In finance, the strong form of the efficient market hypothesis states that studying financial information about stocks is a waste of time since all public and private information that might affect the stock price is already reflected in the price of the stock. However, a study of 450...
  8. AndreasC

    Confidence intervals for ratios of variances and other confusing stats

    Now I don't really know much about the subject, I'm primarily just peaking into my textbook to see how to solve this or that exercise. I believe I can figure out how to solve the third question. However I couldn't find how to solve the first two. I know how to find a 95% confidence interval for...
  9. SamRoss

    I Seeking better explanation of some quantum stats formulae

    In "Introduction to Quantum Mechanics", Griffiths derives the following formulae for counting the number of configurations for N particles. Distinguishable particles... $$ N!\prod_{n=1}^\infty \frac {d^{N_n}_n} {N_n !} $$ Fermions... $$ \prod_{n=1}^\infty \frac {d_n!} {N_n!(d_n-N_n)!}$$...
  10. Biochemgirl2002

    How do i answer this permutation question?

    Question: A home security device with 10 buttons is disarmed when three different buttons are pushed in the proper sequence. (No button can be pushed twice.) If the correct code is forgotten, what is the probability of disarming this device? My attempt: 10!/(10-3)! =(...
  11. BiGyElLoWhAt

    How to store ping results into an array or variable using a batch file

    I don't know much about batch, but what I want is to execute a command such as ping google.com -n 200 and store all 200 ping latency results to a variable. The default results (avg max min %lost) isn't enough for me to tell if I can do what I need to do. I would like to calculate the average...
  12. B

    I Finding CDF given boundary conditions (simple stats and calc)

    I'm not quite sure if my problem is considered a calculus problem or a statistics problem, but I believe it to be a statistics related problem. Below is a screenshot of what I'm dealing with. For a) I expressed f(t) in terms of parameters p and u, and I got: $$f(t)=\frac{-u \cdot a + u \cdot...
  13. J

    I How Are Statistical Tables Created?

    All, https://jimgrange.wordpress.com/2015/12/05/statistics-tables-where-do-the-numbers-come-from/ This is a great post -- but I'm a little foggy on the sentence that says "...mean and standard deviation for each condition is fixed at 0 and 1." Can someone explain this in a slightly different...
  14. E

    B Generating Stats and Probabilities

    Hey everyone, So lately, my friends and I have been playing a card game (magic, because we're nerds :P) and we've been trying to rank our decks (as well as our probabilities to win a game, a match, etc). I've begun working on a spreadsheet with some initial data points (about 30 in total). The...
  15. C

    I Stats Q Help: Find Probability of Contaminated Cherry Pies

    Hi, my main sticking point with the following is which bit of statistics/probability theory is needed to answer the question. We've only been taught basic Bayes theory, the standard pdfs and a little on hypothesis testing. I have spent way too much time just trying to figure out where to start...
  16. A

    MHB Stats question on premiership goals

    I'm doing 1st year IT in uni and have maths questions which are beyond me, please help! Question 5 is causing me issues!
  17. H

    [Poisson Stats] Error on half-life for radioactive decay

    Hi there, not sure whether this is in the right section but: I've made two runs of a radioactive decay experiment where I've got a log(N) vs. time plots. From this I've got the decay constants and hence the half-life. I've averaged these two half-lives ( = 160 secs) and now I'm trying to work...
  18. J

    Calculating Mode and Median for Non-decreasing Series | Stats Homework Solution

    Homework Statement Consider non-decreasing series of numbers: 1, 8, 8, 13, 14, 14, x, y, 18, 20, 31, 34, 38 and 40. Median is 15 Calculate mode Homework Equations Median is middle term for odd number of terms and it's average of middle 2 terms for even number of terms. 3 Median = Mode + 2 Mean...
  19. FallenApple

    Admissions Which PhD do I have a better shot in? Stats vs Applied Math?

    So I have a MS in Stats and a BS in Applied Math. For various reasons not related to raw ability, my GPA in Stats turned out to not be so good( 3.4) but my math GPA from undergrad is excellent ( 3.8). Should I even attempt continuing on in Stats or can I start over with a fresh plate in Applied...
  20. R

    A F-test regression test, when and how?

    I am aware that f-tests can be used to check the null hypothesis when comparing regression models if the models are nested. What I am confused about is if I can apply an f-test to compare the following, (and if so what is the best way) I have two regression laws Y = a1*X1 + a2*X2 + b Y =...
  21. S

    Statistics - Batch AQL? (Acceptance Quality limit) HNC

    Hi All, Currently on a distance learning HNC and I am not quite sure whether the question just wants me to answer 'yes' or give mathematical evidence. Part A answered, Part B not sure... Any help would be great! 2. The process for the production of an electrical device is suitable for...
  22. O

    Probability and Stats - Show the Sample Space

    Homework Statement An assembly line is observed until items of both types—good (G) items and items not meeting specification (N)—are observed. Show the sample space. Homework Equations Let G be Good Let N be Not Good The Attempt at a Solution S = {GN, GGN, GG...N, GG..., NG, NNG, NN...G...
  23. A

    I Density, distribution and derivative relationship (stats)

    I am currently enrolled in a statistics course, and the following is stated in my course book with no attempt at an explanation: Suppose that f is the probability density function for the random variable (X,Y), and that F is the distribution function. Then, f_{X,Y}(x,y)=\frac{\partial^{2}...
  24. gelfand

    How Do Mean, Standard Deviation, and IQR Reflect Differences in Data Sets?

    Homework Statement Compare and contrast the given data Homework Equations None needed for this The Attempt at a Solution I'm never too sure what kind of thing I'd be expected to do for something like this. Here's how I would go about it, but would appreciate any pointers / things to...
  25. M

    Probability virus question at different infection rates

    Homework Statement From various studies, it is known that once an individual is infected with a virus, they become infectious at rate λ. The individual will recover at rate λ, independent of the time it took for them to become infectious. Let X be the total amount of time an individual has this...
  26. O

    Portions of Calculus to Review for Intro. to Prob & Stats

    Hey everyone, I'm a CS major, and haven't been using calculus 1 or 2 for over a year and a half now. I vaguely remember any of it other than basic concepts (what derivatives and integrals are, second derivative, inflection points, etc.). I am taking an Introduction to Probability and...
  27. M

    Sample space probability question

    Homework Statement [/B] Driving to work, a commuter passes through a sequence of three traffic lights. At each light he either stops, denoted by s, or continues, denoted by c. Assume that the outcome c or s for each traffic light is independent of the outcome of other traffic lights. (a)...
  28. M

    Probability question with cups

    Homework Statement [/B] There are six pairs of cups and saucers; two are red, two are white and two blue. 1. Ignoring the saucers, calculate the number of distinct arrangements of the cups. 2.Determine the number of distinct arrangements such that no cup is on a saucer of the same pattern for...
  29. Ericamathstats

    Studying Applied math or pure math? + Stats

    Hi, I am wanting some advice on about studying applied math or pure math. I have finished my 2nd year at uni and will be starting my 3rd year soon and have been thinking about changing my major from pure to applied (I also major in statistics as well). After I graduate I would love to do...
  30. A

    Which undergrad comp sci courses would be helpful for stats?

    I'm two semesters away from graduating, after which i will get a masters degree in stats. My last semester is basically just one where i take courses I want while i wait for grad school to start, because i will have graduated after the semester after this current semester. Which COMPUTER SCIENCE...
  31. A

    Calculators How can I plot concentration as a function of time on my TI-84 Plus calculator?

    Hi, I wasn't sure where to post this. I have a chemistry homework problem, which is not necessarily that hard, but it wants me to put values into my TI-84 Plus. I will not explain the problem too deeply, but it's about reaction time, volume, and concentration (mol/L). I am given a table of...
  32. reddvoid

    Synopsys ICC: cell stats and post route netlist from mwlib

    Hi, I have loaded the milkyway database of the design to the synopsys ic compiler how can i get details of all the cells present in the design or the netlist after place and route ? Thanks :)
  33. Kingyou123

    Stats Help Using Standard deviation and a population

    Homework Statement Joan’s finishing time for the Bolder Boulder 10K race was 1.75 standard deviations faster than the women’s average for her age group. There were 405 women who ran in her age group. Assuming a normal distribution, how many women ran faster than Joan. Homework Equations The...
  34. A

    Job Skills Is it worth it to stay an extra year to get a BS in Stats?

    hello. I was originally planning to get a BS in statistics but then i chickened out because i feared that i might not be mathematically gifted/strong enough to get through the program, which would result in me not having the very basic in today's world : a bachelor's degree. So i switched to...
  35. C

    What is the Probability of Hereditary Conditions in a Gaussian Distribution?

    Homework Statement Please help! I'm new to Gaussian and I've been on this problem for hours, I can't crack it at all (no pun intended) can anyone provide a detailed walk through the answers? On average 5% of eggs contain a hereditary condition. Use Gaussian distribution to find the...
  36. C

    I What is the Probability of a Sample Having Access to Clean Drinking Water?

    Getting ahead with my S1 & S2 for my further maths mods next year, really stuck on this particular question, as there is no such successive trials etc, please help me solve, so i can make some actual sense of what the hell is going on! Cheers, roughly that the portion of families with access...
  37. M

    What values of k make the proportion of observations with |di| ≥ k meaningful?

    Homework Statement Given that r≥(n-1)/(k^2) a) Show that the proportion of observations for which |di | ≥ k cannot exceed 1/(k^2) b) For what values of k is this meaningful.The Attempt at a Solution [/B] a) (r/n)≥(n-1)/(n*k^2) (r/n)≥(n-1)/(n*k^2) (r/n)≥(n)/(n*k^2) -1/(n*k^2)...
  38. M

    How Do You Convert Body Temperature from Celsius to Fahrenheit in Statistics?

    Homework Statement (1) Let the random variable X be the body temperature in ◦C for a randomly chosen person during waking hours. X is assumed to be a normally distributed with mean E(X) = 37.5 and standard deviation sd(X) = 0.3. Let Y be the body temperature in ◦F for a randomly chosen person...
  39. M

    Probability insurance company problem

    Homework Statement (4) (a) Let X be a random variable defined by the probability mass function P(X = x). The possible values X can take (denoted x) and the probability of those values occurring P(X = x) can be seen below x 0 1000 2000 5000 P(X = x) 0.94 0.03 0.02 0.01 Find E(X). (b) An...
  40. M

    What is the expected profit for a car rental insurance company?

    Homework Statement (4) (a) Let X be a random variable defined by the probability mass function P(X = x). The possible values X can take (denoted x) and the probability of those values occurring P(X = x) can be seen below x 0 1000 2000 5000 P(X = x) 0.94 0.03 0.02 0.01 Find E(X). (b) An...
  41. M

    M&Ms Probability Help: Understanding P(B|A) in Random Selection Scenarios"

    Homework Statement [/B] A bowl contains a large number of M&Ms. A single M&M is chosen at random, its colour is observed, and then it is returned to the bowl. A second M&M is chosen at random and its colour is observed. Let A be the event that the first M&M is yellow and B be the event that the...
  42. kostoglotov

    Heading power side,do a unit in stats or computation?

    1st year, heading power side, should I do a unit in stats or "computational explorations"? My 2nd semester must needs consist of a foundations of EE unit, a foundations of ME unit, I've picked a unit for building IT systems (since a lot of power side these days involves SCADA and smart grids...
  43. Amcote

    Stats: Approximating a binomial with a normal distribution

    Homework Statement A multiple choice test consists of a series of questions, each with four possible answers. How many questions are needed in order to be 99% confident that a student who guesses blindly at each question scores no more than 35% on the test? Homework Equations So I know that...
  44. Prez Cannady

    Are there any stats on global Internet traffic by protocol?

    Just like it says on the tin. Looking for recent statistics on global traffic by various (preferably application layer) protocols (i.e., DNS, HTTP, SMTP, etc.). Closest I can find are some regional and national breakdowns, but mostly from a lay reader's point of view.
  45. J

    A Stats: would the sum of the variances be 1 in this case?

    Often in empirical studies you see statements that factor X explains some fraction of the variance in some other variable V, and thinking about what this means intuitively made me curious about the following question. Suppose you have a model where the values of some set of factors X1, X2, ...
  46. M

    Stats or Proofs: Which Math Course is More Valuable for a Physics Major?

    I am a physics major deciding between taking either Statistics or Foundations of Higher Mathematics this semester. Neither are major requirments. Foundations of Higher Math covers logic, set theory, proofs, number systems, and some basic analysis. Elementary to Intermediate Statistics and Data...
  47. W

    I think this is about the Central Limit Theorem

    Homework Statement An engineer is measuring a quantity q. It is assumed that there is a random error in each measurement, so the engineer will take n measurements and reports the average of the measurements as the estimated value of q. Specifically, if Yi is the value that is obtained in the...
  48. W

    Cantelli's Inequality and Chebyshev's Inequality

    Homework Statement The number of customers visiting a store during a day is a random variable with mean EX=100and variance Var(X)=225. Using Chebyshev's inequality, find an upper bound for having more than 120 or less than 80customers in a day. That is, find an upper bound on P(X≤80 or X≥120)...
  49. L

    Advice request good study stats along discrete math

    I study a textbook in Discrete Math 7e Rosen , I am in ch.4 Number Theory Mainly for computer science improvement (cs) Is it ok study same time a Probability & Statistics textbook again for cs...? I have background in Calculus I II and Linear Algebra & web development.
  50. W

    Marginal PMG of of 2 random variables with Joint PMF

    Homework Statement Consider two random variables X and Y with joint PMF given by: PXY(k,L) = 1/(2k+l), for k,l = 1,2,3,... A) Show that X and Y are independent and find the marginal PMFs of X and Y B) Find P(X2 + Y2 ≤ 10) Homework Equations P(A)∩P(B)/P(B) = P(A|B) P(A|B) = P(A) if independent...