Questions tagged [mean]

The expected value of a random variable; or a location measure for a sample.

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12 views

Normalize sample to match the mean and the standard deviation

There are two samples (sufficiently large and independent). One, size $n_1$ has the mean $m_1$ and the standard deviation $s_1$, the other, size $n_2$ with the mean $m_2$ and the standard deviation $...
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How to get the “reliability percentage” of a measurement

I need to get the amount of confidence I can have on a measurement (from 0 to 100 percent). In other words, I need to know how much reliable the data on a measurement is for me to trust its ...
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mean , standard deviation finite population [closed]

A sample of 50 observations is taken from a normal population, with mean=100 and standard deviation=10. If the population is finite with N=250. Find: a) 𝑃(𝑋̅>103) b) 𝑃(98<𝑋̅<101) c) ...
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How to calculate the range from mean and SD?

Is is possible to calculate or estimate the range of a population if I know the mean, population size and standard deviation? I am doing a research and the mean age of the population is 29.9 +/- 5.3 ...
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ANOVA with small sample (duplicate)

I have a study with only a duplicate sample. I would like to know if there are differences between the 5 averages, each group has two samples. In another case, I have 3 averages and each group has 3 ...
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Uncertainty of a Mean from measurements with different uncertainties and of different items

I've searched around, but I am just not sure that the explanations I've found quite match up with what I am trying to do. Let's say I have 3 vials of a gas. For each vial, I measure some $T$, $P$, and ...
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Comparing yearly data that has different $n$ values per year?

I have been collecting soil moisture data at my research site for almost 20 years. However, I have not been consistent with the number of times that I have been taken these measurements. The problem ...
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How would a moment generating function change if all the random variables are increased by a value

Suppose you have some moment generating function $M_x(t)$ Now all the random variables x are increased by a arbitrary value b. What is the new moment generating value? I tried solving this by moving ...
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What is the mean absolute difference between values in a normal distribution?

I understand that variance is mean of squared differences and that standard deviation is square root of the mean. What, however, is the average difference between values in a normal distribution (...
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How is it possible for the arithmetic mean of a distribution to be off-center?

This is a question I recently saw on a test: "Consider the following statement: More than 65% of the residents of Los Angeles earn less than the average wage for that city. Could this statement ...
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How can I estimate the distribution of sizes if I sample from the tails of that distribution?

Let’s say I have an insect farm and they lay down a lot of eggs, which I collect in a cup. Now I want to study the size distribution of those eggs, but there’s a problem: The younger eggs, which are ...
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Is there a situation where you cannot do the T-test for mean inference?

So for mean inference, would there be a situation where you cannot use the T-test? Seems like you can always calculate a t-statistic, so it seems like you can always do the t-test for mean inference. ...
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Proportion of the sums or average proportion of the parts?

Here’s a curiosity that come up during a work discussion. While this example uses financial data, it has a statistical question at its heart. Consider the following table with a budget and actual ...
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Acceptable average difference value for scientific literature?

I have two instruments that measure the same parameter, I'll call them 1 and 2. 1 is calibrated and zeroed during the study and 2 is not calibrated and zeroed so the baseline values are all over the ...
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1answer
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Should an observation always belong to the population to calculate its z-score?

It was mentioned in this link that, the standard score is the number of standard deviations by which the value of a raw score (i.e., an observed value or data point) is above or below the mean value ...
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Need help identifying a measure of central tendency, and how much a certain value deviates from it

So, I had asked a previous question for a problem that I am having. But, I don't think I framed it correctly, so I am trying to frame it more clearly here. Essentially, I have a skew normal ...
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Is it necessary for averaging amount of samples per class?

Say I have a mix of data from multiple sources, some classes have data up to around 200 whilst some have around 10~20 samples. (with negative samples ignored) Should I build my training, testing and ...
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Asking the mean of food group that consisted of several food? [closed]

Hello i know this is a very basic thing but i just so confused. So i have several foods in a food group, for instance, for fritters group, i have fried tofu and sausage. I have the frequency (how ...
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Are this simple claim and its proof correct?

Suppose random sequence $\{X_{i}(N)\}_{i=1}^{N}$ is a row-wise i.i.d. triangular array, where $N$ is sample size. This means for any given $N$, $X_{i}(N),\dots,X_{N}(N)$ are i.i.d. following ...
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Paired T-test or Linear Mixed Model or what else?

I have measured 8 different features on the same mice on three different days. I want to compare the means of those 3 days based on the features. I have executed paired T-tests for each feature in the ...
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17 views

Mean then mult or mult and then mean

I have a dataset like the following structure: ...
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What situations using median is not recommeneded?

I was recently asked this question in an interview about when/where not to use median. I know median has some limitations such as it requires ordered list of numbers. But I am not sure if there is any ...
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Why taking an average makes convergence to zero faster?

Let $f(x,y)$ be some density, and let the leave-one-out Nadaraya-Watson estimator $\widehat{f}_{-i}(x,y)$ be defined as follows: $\widehat{f}_{-i}(x,y)=\frac{1}{(n-1)h^2}\sum_{j=1,j\neq i}^nK(\frac{(...
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Basic mean question

Learned today in stats this cool piece of information: If you wanted to optimize the $(y-\overline{y})^2$ or differences squared, of some data. Where $\overline{y}$ is a constant y = number, then you ...
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How can I develop a 0-100 composite or index score using multiple Z scores from multiple independent variables?

I'm really interested in index scores like the human development index or economic freedom index where they rank things on a 0-100 scale based off of a bunch of different variables (e.g. press freedom,...
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Is it valid to conduct a two sample t-test in this situation?

I know this is a real easy question, but I'm a little unsecure based on all that I read. I have a dataset with housing prices across a city. One of the variables also stores the postal-code. Now what ...
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Calculating the variance in throws made by a juggling machine

I have built a juggling machine. It has no sensors and moves in a consistent programed motion. In my attempts to make the machine juggle for as long as possible, I have been studying the accuracy of ...
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Difference between Sample Mean($\bar{X}$) and Expected Value (E[X])

I know this has been asked and answered, but many even have contradictory definitions as to which represents the mean of a probability distribution. I would like to cite: https://stats.stackexchange....
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Why use Welch's T-Interval or Pooled T-Interval For Mean Differences?

Let's say you have two samples from two populations, X and Y. You want to build a confidence interval around the difference in means of the two populations. Why not just always calculate a new ...
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Is regression towards the mean happening when we use a control group?

I have a subset of 40000 participants in my study. From those I would like to study those with higher weight longitudinally, and compare them with those with healthy weight. I observe, that those with ...
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Distribution of sample mean when samples are normal and correlated

For the context of my question, let's say we have a n-dimensional multivariate normal random variable $\textbf{y} = (y_1,y_2,..,y_n)' \sim \textbf{N}(\mathbf{\mu,\Sigma})$ where $\mathbf{\mu} = (\mu,\...
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Same mean but different standard deviation, how to interpret?

Can i just assume they have the same behavior? i need some advice on how i would look at these graphs. Should I use standard deviation to analyse fluctuation or median instead of mean? or can i just ...
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How to interpret two graphs/data with the same mean but different standard deviation?

I have two lines with the same average, but has more fluctuation, do i analyse them in the same way and make conclusion? Basically i need some advice on how i would look at these graphs. Should I use ...
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How to scale/trasform data for low sample event

A group of users search a keyword on a search engine, they click the web page and a few of them purchase the product (lead). I have to calculate the conversion rate (lead/clicks). Now, for keywords ...
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Estimation of means and variance from 10 independent samples of varying sizes

Consider a stochastic computer simulation that outputs a unique integer value x and a unique float value y. I am trying to ...
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49 views

Data normalization by using mean and standard deviation - Strange example

I read a paper which talks about two samples; the first one concerning data (e.g. resistance $R_{ct}$) from a biosensor1 (called module), the second one concerning data from biosensor2 (called CHI). ...
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Mean centering my data for regression

Can I mean-centre my data and then calculate the percentage change or is that redundant? For instance, I want to perform a regression on my data. I have my participants IQ score, which I mean-centered ...
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For real variables, variance is to entropy, what the mean is to -?

If $X$ is a real random variable with a pdf, variance/standard deviation is a measure of $X$'s dispersion about the pdf's central tendency, which in turn is referred to as the mean of $X$. For many, ...
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Does it make sense computing the mean value of a set of MSE values?

First of all, thank you for your attention. One of my class projects asked me to quantify the asymmetry of 3 classes of moles, given a dataset. In order to do that, I estimated the MSE between a 2D ...
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$\sqrt{n}$-consistent and strongly consistent

Can you show that $\bar{X}$ is a $\sqrt{n}$-consistent and strongly consistent for $\mu$? Where $X_1, X_2,..., X_n$ be iid from $P\in{\wp}$ and $\mu$, mean of $P$ is assumed to be finite.
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Convergence of bootstrap standard error estimate (one of the problems from Efron's book)

I am trying to solve problem 2.5 from the Efron/Tibshirani book, An Introduction to the Bootstrap (page 16). The problem asks to show that by applying the weak law of large numbers, the bootstrap ...
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1answer
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Compute means using number of observations and standard deviation

Is it possible to compute mean using standard deviation and number of observations?
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Use t-distribution for sample mean of uniform RV's [duplicate]

Given there are 10 RV distributed by $U[0,\theta]$ ($\theta$ supposed to be uknown).I know sample mean ($\bar{X_{10}}$) of and sample variance ($\hat{s_{10}}$), can I found 95% CI for mean? My answer ...
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How to interpret standard deviations when comparing two variables (when taking log)?

I'm comparing two models, in one model I take the log of one of the independent variables (in the other I don't). I've compared R squared values, but I also want to compare the variables themselves. I ...
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34 views

Calculate Average Score on Repeated Measures with Uneven Sample Sizes

I am currently evaluating the predictive validity of a set of personnel selection procedures (predictor) on subsequent vocational training outcomes (criterion). As far as the criterion variables are ...
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50 views

How can I calculate the mean and variance of a linearly transformed random variable?

Say I have a random variable $x$, with mean $\mu_x=35$ and standard deviation $\sigma_x=10$. I want to linearly transform $x$ to $y$ according to the formula $y=a+bx$ so that $\mu_y=100$ and $\sigma_y=...
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one-sided t-test after a two-sided t-test?

I have two groups and I conducted a two-sided $t$-test. mean group 1: 3.79 mean group 2: 4.07 $p$-value: 0.0081 The $p$-value is less than $\alpha$ = 0.05, hence, I can reject the null hypothesis of ...
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24 views

Calculating standard deviation without original measurements

Assume I have the monthly data for the price of items like this: num_items = [10, 22, 13, 4, 15] avg_cost = [200, 103, 143, 412, 123] Now, I do not have the original list of item-wise cost table. From ...
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Can trials have a differing number of samples when running PCA ? Why not?

Can somebody confirm that the number of "samples for each trial" doesn't matter(i guess that's right the language) for PCA. The case at hand is this: i have 5 sets of 3-dimensional ...
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The impact of geometric and arithemtic mean on heteroscedasticity

assuming I have a time series and want to do a regression on it. I see that the residuals are heteroscedastic, e.g. that the variance is proportional to the mean. A remedy for this is/can be the log-...

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