# Questions tagged [means]

In probability and statistics, mean and expected value are used synonymously to refer to one measure of the central tendency either of a probability distribution or of the random variable characterized by that distribution. For a data set, refers to a central value of a discrete set of numbers: specifically, the sum of the values divided by the number of values.

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### Recalculate average based on subset of poisson distribution

Assuming a series of independent events, probability of the event occurring on a given day is a poisson distribution with λ=0.8. This includes probability of event ...
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### Standard Deviation and data set increasing by multiplication.

Hi guys I recently started learning statistics and I'm a bit confused. I know when a data set is multiplied by a constant, its standard deviation and mean is multiplied by the same number. However ...
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### Choosing the correct t test for comparing two sample means

Six sets of identical twins were divided at random into two groups, each group containing one twin from each set. The first group was taught some basic statistics by method A and the second by method ...
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### Expectation Value and Variance

I know the formula for Expectation value is $$E(X)=\sum f_ix_i$$ where $f_i$ denotes the PMF(Probability Mass Function) and Variance is $Var(X)=E((X-m)^2)$ where m is E(X). But what is really the ...
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### Geometric mean with negative numbers

I want a workaround for the geometric mean when the data contains negative numbers. I found this on Wikipedia, but it doesn't work if m is odd and there is an even number of data points. What should ...
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### A Hypergeometric probability distribution and Zeilberger

On page 107 of book 'The Concrete Tetrahedron' by Manuel Kauers . Peter Paule A Hypergeometric probability distribution is given : consider an urn containing N balls, m green ones and $N - m$ blue ...
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### What are the geometric, harmonic, and quadratic averages of a function?

In Mean of a function, they describe the arithmetic mean of a function and at the bottom of the article they said: There is also a harmonic average of functions and a quadratic average (or root mean ...
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### Sample Mean vs. Population Mean

I'm having trouble understanding what exactly is meant to be found given the information presented. Obviously, the answer will be a value found on the z-table and the probability of this event ...
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Suppose I have $n$ integers $\mu_i$ , $i=\{1,2,...,n\}$. Define $\bar{\mu}=\frac{1}{n}\sum_{i=1}^{n} \mu_i$. It is given that all the $\mu_i$'s are either $+1$ or $-1$. How can I show that $\sum_{i=1}^... • 429 0 votes 1 answer 37 views ### Derivation of Inequality of arithmetic and geometric means using a circle $$a,b:=\text{positive numbers}\tag{1}$$ I want to derive the following inequality. $$\underbrace{\sqrt{ab}\leq{a+b\over 2}}_{\text{Inequality of arithmetic and geometric mean}}\tag{2}$$ To derive it, ... 0 votes 1 answer 38 views ### Statistics test question about a mean The following question from a Statistics test does not make sense to me. Question: Data from the past 100 years show that rainfall during April varies randomly from day to day. Over that period the ... • 203 0 votes 1 answer 32 views ### Is the geometric mean bounded above by this value? It is clear that the geometric mean is bounded above by the arithmetic mean: $$\prod_{k=1}^{M} x_k^{\alpha_k} \leq \sum_{k=1}^{M}\alpha_k x_k$$ Moreover, it is clear that the arithmetic mean is ... • 507 0 votes 0 answers 21 views ### Does the population variance equal the variance of a single observation? According to Wikipedia, the standard error$\sigma^-_x$of a sample mean can be computed by$\frac{\sigma}{\sqrt{n}}$, where$\sigma$is the standard deviation of a statistical population and$n$is ... • 1 1 vote 0 answers 30 views ### What is the notation for the mean of$y$in the$i$-th quantile of$x$? I would like to add the appropriate mathematical notation to use in a figure. I have two original quantitative variables,$y$and$x$, named “long variable name$y$” and “long variable name$x$”. I ... 1 vote 0 answers 27 views ### Standard error of the mean for different experiments I am confused about the calculation of the SEM when one performs multiple independent experiments. Suppose we perform$k$different experiments obtaining means$\mu_k$, standard deviations'$\sigma_k$... • 11 0 votes 0 answers 25 views ### Obtain standard deviation from sum of values I'm looking for a way to obtain the "composed" mean and standard deviation of two (related) datasets. So let's assume I have n = 25 recordings of one characteristic (x) and the same number ... 0 votes 0 answers 25 views ### standard deviations for mean vs for predictions I work in finance and wanted to ask a quick question regarding standard deviation of data sets. I have collected data sets over the last 10 years and would like to use them to make a prediction for ... 0 votes 0 answers 24 views ### Is this a Mean? Recognizing functional form of a generalized mean. Can the operator $$(f')^{-1}\left(\frac{f(y)-f(x)}{y-x}\right)$$ be interpreted as a mean and if so, does it have a name? If$f(x)=x^2$then this simplifies to \begin{... 1 vote 0 answers 24 views ### Can we use power mean to generalize min and max for complex numbers? Power mean$M_p(a,b)$of order$p \in \mathbb{R}$for a pair$(a,b) \in \mathbb{R}^+$is defined as$M_p(a,b)= \Big(\frac{a^p+b^p}{2}\Big)^{\frac{1}{p}}$. For example$p = 1$gives arithmetic mean, ... • 98 0 votes 0 answers 10 views ### Calculating$Cov\left(\overline{Y}_j,\:\overline{Y}\right)$for a basic one-way model Consider the basic one-way model: I want to show that$Cov\left(\overline{Y}_j,\:\overline{Y}\right)=\frac{\sigma ^2}{na}\$. I derived the following expected values: $$E\left(\overline{Y}_j\right)=\mu ... 0 votes 0 answers 13 views ### What test to use to see the difference between two groupps with the same variance? I have the data for 3 groups A,B,C with the times of run of 5 kilometers.  \begin{matrix} Group A & Group B & Group C \\ 27.5 & 35.3 & 45.8 \\ 30.6 & 40.2 & 42.6 \\ 28.5 &... 0 votes 0 answers 49 views ### How to evaluate the difference/distance between 2 values positive and negative on a scale Problem 1 : The input is 2 values, that can be in a scale between [-3.89, 10.66] And i need to compare the difference between an oldValue (A) and a newValue (B). So i want to create a variable that ... • 1 0 votes 0 answers 51 views ### Sum of deviations from mean and Mean deviation around mean We know, Sum of deviation of variate from their A.M. is always zero that is \sum(x_i- \mu) where x_i are all the elements and \mu is the arithmetic mean. Also mean deviation is the mean of the ... 0 votes 1 answer 36 views ### Standardising third moment I am assigning values to objects in a process. I would like the values to end up being normally distributed with variance one. For this I standardise them by subtracting their average from each and ... 0 votes 0 answers 25 views ### Test statistic of sample mean of non identical Gaussians It is well known that given iid gaussians Y_i \sim \mathcal{N}(m, v^2), with unknown mean and variance, then t = \frac{\hat{m}-m}{\hat{v}/\sqrt{n}} follows a student-t distribution with n-1 ... 1 vote 0 answers 22 views ### Is there any mathematical relation between a harmonic mean and the harmonic mean of shifted values? Let H be the harmonic mean of a set of reals x_i. Can we say anything about the harmonic mean H' of the same set of values, but for which each value is increased by a constant c\,? That is,$$...
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For a one-sided distribution such as Poisson or the exponential distribution (but not specifically those particular one-sided distributions), $$p_x(\alpha) = 0 \qquad \forall \alpha<0$$ is there ...