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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Distribution of sample means explanation

Say a casino has N slot machines all with the same expected value and standard deviation. Why is it when the standard deviation gets really large you end up with more machines under the expected value than over? I understand that the average of the…
ndm
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How to calculate percentile rank if all values are equal to zero

The formula for finding Percentile rank as per wikipedia is $$\frac{c_{\ell}+0.5 f_{i}}{N} \times 100 \%$$ One of the edge cases in my application is when all the values are zero. In this case the number of scores less than the score of interest…
ganeshran
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Determining the mode or median in a statistical survey of a continuous variable

we learned in school that the rule to determine a mode in a statistical distribution of a continuous variable is Mo=Lower boundary of modal classe+(fmo-fb)/(fmo-f before+fmo-f greater) ×class width. Actually, I wasn't convinced because there is no…
user448075
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Does a one tailed test statistic will always fail to reject the null if observed value is in the tail opposite to the alternative hypothesis?

Suppose: $H_0: \beta \le 0.5$ $H_1: \beta > 0.5$ $\widehat \beta = 0.49$ If $\widehat \beta = 0.49$ and I want to test the alternative hypothesis that $\beta > 0.5$ (versus the null that $\beta \le 0.5$). Won't it be the case that a one tailed t…
J Doe
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Random simulations of the distribution of genders in a classroom

For my AP statistic class, we had to design an experiment (usually a survey of what brand of soda people prefer), so me being an overachiever decided to study how boys and girls distribute themselves among other genders. For instance, girls will sit…
Jacob Claassen
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Do multiple polls with identical margins of error decrease the total margin of error?

Is it possible to take multiple polls and combine their margin of error to produce a single, overall margin of error? For an example, let's say we have two populations with the following characteristics, obtained from similar polls: Population A…
Logical Fallacy
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Why doen't we consider nonlinear estimators for the parameters of linear regression models?

The Gauss-Markov theorem tells us that the ordinary least-squares (OLS) estimator is the best linear unbiased estimator (BLUE) for the coefficients in a linear regression (given some conditions on the errors). I can understand why we want an…
user126350
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How do you find the number that corresponds to Quartile 1, when given an even number of scores?

If you have an odd number of data values {39, 40, 42, 44, 47, 48, 49, 51, 53}, what is the score that value that corresponds to Quartile 1? In general, I would like to know if you include the median's value (47) in figuring the position of quartile…
kuttaka
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Skewness-adjusted t-statistic

I've come across two different forms of a skewness-adjusted t-statistic, which was developed originally by Johnson (1978): $$ J = t + \frac{gt^2}{3n} + \frac{g}{6n} $$ and $$ J = t + \frac{gt^2}{3\sqrt{n}} + \frac{g}{6\sqrt{n}}, $$ where $t$ is the…
Dave
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Expected Mean Squares for Two Factor Experiments

I am looking at two-factor experiments with fixed factors. I've seen that for MSE, the expected value is $\sigma^2$. For E(MSA), E(MSB), and E(MSAB) I think these will be linear combinations of $\sigma^2$ such as $\sigma^2$+ something. How can I go…
user408688
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Determining a value $k$ that gives a size = 0.05 test.

A single observation $X$ from a normal distribution with mean $\mu$ and $\sigma^2$=1 is used to test $$H_0 : \mu = 1 \ \ \ \text{vs} \ \ \ H_1 : \mu \lt 1 $$ using the critical region $C = {{x : x \lt k}}$ Determine the value of k that gives a size…
pkfly103
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The Normal Distribution

I'd like to correct some of my misconceptions about The Normal Distribution. Firstly, I don't know how to interpret the following formula: $ \displaystyle Z = \frac{X-\mu}{\sigma}$ I was first introduced to this formula in a earlier chapter and it…
efwererrerwerrwerwer
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Statistics of a racketball/volleyball/badminton game

It's been a while since I've used my knowledge in statistics and I have no idea how to turn that problem into an equation. I wanted to challenge myself but I failed. I thought maybe you too would like this challenge. Starting with pre-defined score…
Frank Malenfant
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Finding z-score of probability

I am learning the finance topic value at risk and trying to understand the number of standard deviations. I dont quite get why was 1.65 used to multiply against the std dev instead of 1.644853 as shown in the calculator below (used to retrieve the…
ilovetolearn
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Is following function valid to be a copula function?

I know $C(u,v)=uv$ is a copula corresponding to the independent case. How about $C(u,v)=u^2v^2$?
ndor
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