Mathematics Stack Exchange
Mathematics Stack Exchange

Questions tagged [statistics]

Mathematical statistics is the study of statistics from a mathematical standpoint, using probability theory and other branches of mathematics such as linear algebra and analysis.

Statistics is the science of the collection, organization, and interpretation of data. It deals with many aspects of data, which includes the planning of data collection in terms of the design of surveys and experiments. (From Wikipedia)

More specifically, mathematical statistics is the study of statistics from a mathematical standpoint, using probability theory as well as other branches of mathematics such as linear algebra and mathematical analysis. (From Wikipedia)

For questions which are more generally about collecting and treating data, it is advised that you post your question on Cross Validated and DSSE.

37109 questions
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Dividing Variance by $n$

This sample follows a Normal Distribution with Mean $= 280 / 20 = 14$, and Variance $= (3977.57 / 20) - 14^2 = 2.88$. To find the unbiased variance, we can divide it by $19$ to get $3.03$. However, in the following question: I used…
StopReadingThisUsername
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Motivation Of Correlation Coefficient Formula

Definitions correlation coefficient $= r = \frac{\sum_{i=1}^{n}(x_i - \bar{x})(y_i - \bar{y})}{\sqrt{\sum_{i=1}^{n}(x_i - \bar{x})^2\sum_{i=1}^{n}(y_i - \bar{y})^2}}$ My Question What is the motivation of this formula? It's supposed to measure…
Dunka
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Balls in a box probabilities

A box is filled out by $1,000$ balls. The box can be thought of as containing $V$ sites and $V$ balls, with $V=1,000$. The box is repeatedly shaken, so that each ball has enough time to visit all $1,000$ sites. The ball are identical, except for…
Alex Trent
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How to explain to non-mathematician what statistical significance is?

Recently I faced with the problem, and I can't explain it to my colleagues. The thing is, that they want to conduct a surveys with one question and the question may have only two answers, and they ask me how many surveys conducted is enough for the…
oleg
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What gives rise to the normal distribution?

I'd like to know if anyone has a generally friendly explanation of why the normal distribution is an attractor of so many observed behaviors in their eventuality. I have a degree in math if you want to get technical, but I'd like to be able to…
Dean Radcliffe
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Sample joint density conditional on sufficient statistic depends on parameter for uniform distribution

Lex $X_1, X_2 \sim U(0, \theta)$ i.i.d , then obviously the sufficient statistic would be $T = \max\{X_1, X_2\}$, which can be easily proven by factorization theorem. However, I try to compute the density $f(x_1, x_2\mid t)$, which turns out to…
Xiaojie
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Confusion on the meaning of confidence interval

The standard deviation of test scores on a certain achievement test is 10.9. A random sample of 60 scores on this test had a mean of 72.1. Based on this sample, find a 95% confidence interval for the true mean of all scores. The formula for…
user133466
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Standard Error, why divide by square root of 2?

I am currently reading the book Options, Futures and Other Derivatives from John C. Hull. In the Chapter of Introducing the Balck-Scholes Model, it says: The standard error of this estimate can be shown to be approximately …
Stephen Ge
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Uniform Distribution vs Exponential Distribution + Confidence interval

Let be a $pdf$, $f(X)$, with exponential distribution and other $pdf$, $f(Y)$, with uniform distribution. I realized, 5000 times, for each one respectively that follow: I used the R to generate a random sample of size $n = 5$, of the random variable…
juaninf
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Rating system incorporating experience

I am looking to rank players on something and right now I am using a win-loss percentage to "rank" the players. The issue is that I have some people who just beat out the 5 game threshold and have a win/loss ratio of say 5 wins, 1 loss for 83% and…
ParoX
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Rounding of complementary percentages

This problem arose while tallying votes in a poll and displaying the results as a whole number percentage. So if "Option A" received $300$ votes and "Option B" received $100$, the display should read "$75\%$, $25\%$". There is a requirement that the…
Peter Gibson
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How to derive Population Variance formula?

There's a formula of variance on wikipedia, but I'm confused with the last equality. How does it come out? $$\sigma^2 = \frac{1}{N} \sum_{i=1}^N (x_i-\mu)^2 = \left(\frac{1}{N}\sum_{i=1}^N x_i^2\right)-\mu^2 = \frac{1}{N^2} \sum_{i
user348218
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98% confidence interval

For this question from a large amount of data I have calculated that the mean is 44.22, the sample size is 100 and the standard deviation is 22.0773. From this I am asked to , make the 98% confidence intervals for the (1) true mean µ of the module…
P.Math
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Mode for unique numbers

I'm trying to construct a rough statistical software and I'm confused about the following: What is the mode if all numbers are unique? What is the mode if 2 numbers have same (highest) frequency? What I feel: Should output nothing. Should output…
Inquest
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Populations and Sample Spaces

I have been reading the book "Introduction To Statistics, A Customised Edition of Statistics For Business and Economics" by P. Newbold et al. As I understand their statement of classical probability: ...Classical probability is the propertion of…
Jimbo
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