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.

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Normal Approximation formula - Why 12?

I've recently begun learning the Mann-Whitney U test and have had to use normal approximation. The formula is straight forward, but I find myself wondering why you use 12 as the denominator in the square root portion. I enjoying knowing where…
Toast
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Quartiles when all numbers are same

I understand quartiles are to be used in large data sets. But for pedagogical purposes, What would be the Quartile1,Median and Quartile3 for a set consisting of same numbers? What would be the quartiles of 7 times 3?
Srini Vas
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Compute the probability that $ | \bar{X} - \mu | > S$

Given $X_1, \ldots, X_n$ from $\mathcal{N} (\mu, \sigma^2)$. I have to compute the probability: $$P\left(|\bar{X} - \mu| > S\right)$$ where $\bar{X}$ is the sample mean and $S^2$ is the sample variance. I tried to expand: $$P\left(\bar{X}^2 + \mu^2…
Aslan986
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measuring the regularity of a grid

I'd like to find a method for scoring the difference in regularity of points in grids - there are two examples below (left) a relatively well ordered grid and (right) a relatively disordered grid. I have a brutish method which analyses nearest…
danodonovan
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Is the p-value the probability that your null hypothesis is true?

I know that the p-value is the probability that the measurement takes a value that is at least as unlikely under the null hypothesis as the observed value. Furthermore, the null hypothesis is rejected if and only if the p-value of the observation is…
user235238
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Which correlation coefficient indicates the strongest relationship between two variables?

I'm trying to understand correlation coefficients, and seem to be missing something. For example, Correlation coefficient: Indicates the direction, positively or negatively of the relationship, and how strongly the 2 variables are related. I…
Anitra Parks
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Cumulative Distribution Function calculation

I've got a question here that I've been working and I've ran into some difficulty. "Let X be a mixed random variable with distribution function: F(x) = 0 if x < 0 cx + 1/4 if 0 <= x < 1 (c is some constant) 1/3 if 1 <= x <2 1 if x >=…
user64219
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Finding conditional probability with Gamma distribution

While I tagged this question homework, it's not really homework. I'm really studying for a test and don't understand how to do something. I have the answer to the question, so the important part is for my to understand how to get there. X has…
kralco626
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Finite Population Correction on sample size

Estimate of percent of an infected species is accurate to within $\pm 0.04%$ with $95\%$ CI Between $15\%$ and $35\%$ of the population are infected Size of the population is between $1100$ and $2300$ Calculate the sample size. My calculations: For…
Tree
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involving exponential distributions

The question states: Let X = time between calls to a service center, It is known that X follows an exponential distribution with a mean of 15 minutes, part 1. What is the probability that x is greater than 20 minutes. So far this is the only one I…
franklin
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Can this statistics question be solved as it stands?

I have been presented with the following question: An attorney claims that more than 25% of all lawyers advertise. A sample of 200 lawyers in a certain city showed that 63 had used some form of advertisement. At $\alpha$ = 0.05 is there enough…
franklin
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elementary t-test question

Q: A tire manufacturer wishes to compare the tread wear of tires made of a new material with that of conventional material. 10 Cars are driven 40,000 miles as the sample set. the following data is obtained: (To avoid some confusion and messy tables…
franklin
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Example of a distribution with mode undefined

Is there any distribution with an undefined mode? If all the elements of the data set have frequency 1 is the mode undefined or all the elements are modes of the distribution?
LoverOfAbstraction
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Variance of function-valued random variables

I am struggling with abstract definitions of basic statistical concepts. For a random variable $X$ which we assume to live in a real Hilbert (or even Banach) space $\mathcal{H}$, its expectation is defined as an element $\mathbb{E}[X] \in…
johnny
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An equation that occurs in ecology

In the field of ecology, a well known relation between the number of species and the size of an island can be approximated by a power function of the form: $S = c A^z$ $S$ = number of species $c$ = a fitted constant $A$ = area of the island $z$ =…
S. Berman
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