Questions tagged [mean]

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

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Is there a standard error of the mean for when population size is known?

Background Let us suppose that we are sampling from a finite population which is itself drawn from a univariate normal distribution. This accomplishes (1) having an underlying probability model and (2)...
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Estimate the mean vector and the covariance matrix using the simple returns

I would appreciate help with how to to estimate the mean vector and the covariance matrix using the simple returns in R. I have historical (weekly) values of five stocks from a capital market for a ...
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How can the sum of averages of my sample exceeds average of entire population? - market concentration

I want to see what percent of a market of listeners on a livestreaming platform my sample of top 100 musicians with the highest number of average listeners during a given month has. I only have ...
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Measuring variability of log in hours

I'm working on measuring the usage patterns of an app for a population of users. I want to find out if they usually log in at the same hours or if their usage times vary a lot. The variance of the ...
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average of geometric and harmonic means

I have a stochastic simulation model in which three types of mean (arithmetic mean, geometric mean, and harmonic mean) are calculated for three different variables. I run the simulation 1000 times so ...
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Quantile Variance and Mean

As I read articles related to quantile measurements of moments, I only found quantile skewness and kurtosis definitions. However, I couldn't find any quantile estimation of variance or mean. Is it ...
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The distribution function of appropriately normalised trimmed mean $T_n(\hat{F}_n)$

A definiton of functional of trimmed mean: $$ T^{\alpha}_n = (n-\lfloor \alpha n \rfloor)^{-1} \sum_{\lfloor\alpha n\rfloor + 1}^{n-\lfloor \alpha n \rfloor} X_{(i)}$$ A definition of the optimal ...
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Comparing measurements I got from my study with other ones from other studies

First of all I’m sorry if this sounds dumb! I’m really trying. I’m conducting a study on measuring adrenal glands in sick patients (3 measurements - cranial height, caudal height and length - in both ...
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How to know statistically for sure if respondents result on a likert scale is proofing anything..?

I have put a question what flow you get from a digital book, compared to paper from 7 (good) to 1 (bad). I only had 26 respondents, and this is the result: ...
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Intuition for why mean of lognormal distribution depends on variance of normally distributed rv

Let $X\sim\mathcal{N}(\mu,\sigma^2)$, which is a normal distribution. Then, $\text{exp}(X)\sim\text{Lognormal}(\mu,\sigma^2)$, and its mean is $$ \mathbb{E}[\text{exp}(X)]=\text{exp}\left(\mu+\dfrac{\...
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Simple question on statistical comparison of grand/pooled means

My problem: I am comparing the means of means of means in my data set. However, my stats software (GraphPad Prism) doesn't know that these said individual values (the means of means of means) are ...
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How is the difference between 2 normal distributions a normal distribution? [duplicate]

I've learned that if we sum or subtract 2 normal distributions, the result would be another normal distribution with $\mu=\mu_{1}\pm\mu_{2}$ and $\sigma=\sqrt{\sigma_{1}^2+\sigma_{2}^2}$ https://www....
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Difference in means vs OLS regression coefficients

Suppose I have a data set where each row represents a test subject. There's a dependent variable (y) and two binary columns (x1, ...
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Standard deviation on Bimodal data

Standard deviation, whilst it is often used on normal distributions, is it a useful statistic on global temperature, both daily and yearly, given that weight of the data is towards the ends of the ...
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Examining stationarity, mean and variance of time series

Hi guys, I encounter this question for a Business Forecasting module and I am very confused by it. Firstly, this looks like an autoregressive model of order 1. From the looks of it, the φ coefficient ...
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Confidence Intervals for More than One Variable?

Consider the univariate case, suppose we have some sample data on the heights of men and women - we are interested in estimating the average heights of men and women in the population, and the ...
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Should I use Mean or Median? [duplicate]

I am analyzing a set of data (results) that does not follow Normal distribution or any known distribution. In this case, is it better to use (mean) or (median) to describe the result? Thanks
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How to change a variable equation so that one quantity impacts the outcome more than it currently is?

Forgive my lack of vocabulary, I've never formally studied statistics. I'm currently working on a project involving quantifying genres of music, and there are only two variables at play: The Total ...
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How do I get the final mean value of imputed data?

I have run multiple imputations on my data and need to now export a final dataset that I can then calculate the mean of each imputed variable. How would one do this? I can't pool the data straight ...
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Statistics to use on Bimodal data

What summary statistics, mean, median, standard deviation, etc. should be used on a skewed, bimodal, dataset and why? These are almost U shaped in a histogram layout with a slight preference for lower ...
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Confidence in a range estimate, and +- 2sigma rule of thumb

It's common to see people report variability in their realized sample through the $\bar{x} \pm 2s$ range, where $\bar{x}$ is the realized mean and $s$ the realized standard deviation estimate in their ...
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Estimating Standard Deviation from sample mean, median and quartiles

I've been trying to estimate the standard deviation from a sample with N = 8149. I've seen a few alternatives to perform this and they all use the IQR. Here's the sample data I have: ...
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Converting difference in means with standard error of difference to percentage difference with standard error of difference

I have two means with standard errors associated. I am able to calculate difference between the means and standard error of the difference. I can calculate percentage difference. I am not sure how ...
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Estimating the Probability in a statistical analysis

I am carrying out a statistical analysis where I run the simulation (Matlab) 5000 times, to get 5000 results. The objective is to estimate the probability of having a result that is less than or equal ...
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Interpretation problems of linear model with no predictors

Let $Y=X\beta$, where $X=(\begin{matrix}1 & 1 & 1\end{matrix})^T$, $Y=(\begin{matrix}6 & 5 & 4\end{matrix})^T$ and $\beta=(\begin{matrix}\beta_0 \end{matrix})$. Now $X\beta=(\begin{...
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Meta analysis average percentage difference with standard error

I am collecting data on the effect calorie labeling has. Each study provides a value for mean calories consumed before the calorie label and after. Each number has a standard error or deviation ...
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"De-meaning" or "Differencing the mean of..." in mathematical term

In a standard regression literature, the following terms are used almost interchangeably and are used also loosely: "De-meaning the equation gives..." "Differencing the mean of the ...
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Should I remove 0 values when calculating the average of many simulation runs?

Let's say I have a simulation model with stages A, B, C. I want to calculate the average time of each stage over 1000 runs as they contain stochastics. In many runs, either one of these stages may not ...
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Accuracy failure example

I am trying to understand the functioning of accuracy and I need a practical example. This is what I understood: it gets the average correctness of the predictions and in some cases its result can be ...
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Expectation of a random variable with positive density at infinity?

Let $X$ be a continuous random variable with pdf $f(x)$. Assume that $f(x) \geq 0$, for all $x > 0$, so $X$ is a positive random variable, $f(\infty) > 0$, i.e. $X$ has a strictly positive ...
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What is the best way to calculate a weighted average that favors rarity?

DISCLAIMER: I am coming from a coding background so I have no doubt I am butchering the terms or what I am trying to ask I am working on a coding project to look at a user's list of movies watched and ...
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Can non-parametric data have mean value and standard deviation?

I understand that for non-parametric data, the probability density function (pdf) cannot be obtained using parameters like (mean value) and (standard deviation), and I understand that we use Kernel ...
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Mean and Variance of an estimated squared proportion from a Binomial distributed random Variable

I want to make a confidence interval on the number of successes $K$, given a sample number $n_2$ and a proportion $h$, where the $K$ would be Binomial distributed. $$ K \sim Bin(n_2, h) $$ However, ...
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Comparing the width of two percentile intervals

Suppose I calculate 99% percentile intervals for two different sample sizes, for example N=10 and N=1000 by doing the following: I take 1000 samples of size N=10 from the population (not bootstrapping)...
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If we numerically code the categories of an ordinal variable, then can we determine its mean as in Likert scale?

Can anyone clear my doubts about 2 things. Doubt1)A dataset of Ordinal type having 2 modes, then does it mean that such dataset have 2 central locations ? Doubt2)As We know that we can not determine ...
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Variability and mean

I am working with future climate change scenarios and I end up with this question. Is it expected from a statistical perspective that a change in the mean goes hand-in-hand with a change in the ...
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How to sort individual tasks by duration when the only available data is the duration of two tasks together?

I have 2 sets of tasks, $S1$ and $S2$. A task can only belongs to one of the set (the intersection is empty). There is 21 differents tasks in $S1$, 57 in $S2$. A task from $S1$ is always followed by a ...
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Is it possible to find the 99th percentile using other percentiles?

I have the 10th, 20th, 25th, 30th, 40th, 50th (I assume this is the same as the mean), 60th, 70th, 75th, 80th and 90th percentile values of a data set. This is for the distribution of salaries in the ...
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finding central tendency

The following table presents frequency distribution of teachers of 1 year: Rank ----------Frequency Professor ------------7 Assoc Professor ------4 Asst Professor--------3 Instructor -----------5 ...
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Is the mean posterior fit the same as the fit of the mean parameters?

Say we are fitting a parametric model $y(x, \theta)$ to some data (e.g. logistic regression). Given a prior distribution over the model parameters $\theta$ and observed data $x$, we arrive at a ...
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Conflict Between Confidence Interval and P-values - One Sample T-Tests

I'm conducting one-sample t-test using R. I calculated p value, effect size, and confidence interval, but they seem to be conflicting. Here is a sample code and output: ...
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Valid confidence interval for the mean of the average of N iid beta-binomial random variables

Let $m,n,l$ be three integers, and, for $i=1,\dots,N$, let $C_i\sim\frac{1}{m}\text{Binom}(m,\mu)$ where $\mu\sim\text{Beta}(n+1-l,l)$ be i.i.d. beta-binomial random variables. Let $\bar{C}=\frac1N\...
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Calculating confidence interval for binomial distribution [duplicate]

Suppose we have a sample $X_1, X_2, \ldots, X_n \stackrel{\text{iid}}{\sim} Binomial(\theta)$, where $n$ is known to be large. I would like to calculate the 95% confidence interval for $\theta$, and I ...
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Can mean be less than half of median if all numbers are non-negative?

I feel like I might be missing something dumb, but in a set of non-negative numbers, is it possible for the mean to be less than half of the median? Example: there are 999 numbers and we are told that ...
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Calculating average for each individual or not?

I have a question about how I should organize my data before doing some statistical analyses. In my data, I have a sample of rats for which the level of tear stains and body lesions is measured. They ...
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Descriptive statistical metrics of RMSE, MAE and R2 on cross-validation and holdout testing

I've tuned 100 models of each one LASSO (Least Absolute and Selector Operator) and Random Forest regression methods. I mean, to predict a hypothetical dependent variable, I've tuned 100 models for ...
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3 votes
1 answer
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How does the 30% trimmed mean of this equal 6.167?

[6, 3, 7, 11, 5, 3, 8, 7, 2, 6, 9, 13, 10, 4, 3] So I'm going through some revision for stats, one of the questions asks to find the trimmed mean of the above data. I've worked it out but my answer ...
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1 vote
1 answer
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conditional quantile and conditional expectation

I was reading some papers and I found some parts are tricky to understand. Assume I have price data , what does it mean to calculate the conditional mean of the price data given yesterday price ? ...
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the two step approach

I have a continuous variable which is not normally distributed i want to transform it to normal using the two step approach method in the link below: Abstract This article describes and demonstrates ...
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How much compensation is needed to take on risk?

We roll three, 8 sided dice. If same face appears 3 times we win 80 dollars. We have a bank of 10,000 dollars. How much are we willing to pay to play? What if we increase the prize to 80,000 dollars? ...
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