Questions tagged [mean]

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

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Doubt about level of confidence

I run 100 simulations with CI at 99% and different seeds. For each simulation I created a report that contains different performance indexes (means) with their CI. However, I noticed that one index ...
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Does it make sense to calculate Relative Standard Error using population parameters?

Relative Standard Error (RSE) is one of the main measures to assess the quality of survey indicators. If only sample data are available, RSE can be computed using estimated mean $\bar{y}$ and ...
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Stat sig results on underpowered experiment

I ran an experiment that was powered enough to detect lifts of 1% on my 2-sample test. Make it really simple: I have two normal distributions and want to compare the means, so I ran a 2-sample t-test ...
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Why don’t we calculate the average of an entire given population instead of computing confidence interval to estimate the population mean?

We compute confidence intervals to estimate the true population mean of either a sample (when population standard deviation is unknown) or an entire population (when population standard deviation is ...
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Verify relationship between a categorical and numerical variable

I have got some data about movie directors and number of cuts per minutes in their movies. I whould like to verify if there is any relation between this two variables. I have tried looking at the mean ...
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Different Number of Judges Scoring and how to Rank

I have looked everywhere and I am struggling to find a solution. Granted, I am no statistician but I do have some knowledge of basic statistics. Any help is truly appreciated! There are a number of ...
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Computing Variability Independent of mean; differences in calculation methods

This question is mostly about another post here on stats.stackexchange. In general, VIM (Variability Independent of the Mean) is usually calculated, as the name suggests, to calculate the variability ...
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Find mean value of total N with only relative frequency and mid point histogram [duplicate]

I have the following data of number of vouchers redeemed : How can i calculate the mean value of total vouchers?
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Is winsorizing limited to the usage of a certain percentile cutoff?

The Context My dataset consists of 68 groups, each with 4 data points inside it. As means of a robustness test, I am looking to see how the type of average/mean I use impacts the analysis that I will ...
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Help with table interpretation

I am an agricultural genomics student and I need help understanding this table of statistics from a study of 1340 cows. can you please explain to me what it means when the mean value is 0? and how to ...
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Formula to determine when mean is stable

I have a sample of values. Every day the sample grows because new values will be added. Every day I calculate the mean of these values. For research purposes I want to know the day that the mean ...
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Bootstrap Standard Error vs Standard Error from sample

For doing inference of a population parameter from a sample, under which examples is better to calculate the standard error using bootstrap distribution of the mean than directly using the standard ...
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Comparison of total counts vs. comparison of mean counts per participant in exploratory data analysis

I already came across this question: Difference in means vs difference in proportions, but could not answer my question based on the answers and comments there. My question would be this: Suppose ...
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We have a sample of random variables constructed from the Euler Maruyama scheme of a stochastic model, is it idependent and identically distributed?

We have the mean reversion stochastic model $dX_t=(\alpha-\beta X_t)dt+\sigma X_t dB_t$, the Euler-Maruyama scheme for this model is $X_{t_i}=X_{t_{i-1}}+(\alpha-\beta X_{t_i})\Delta+\sigma \sqrt{\...
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What is the distribution of random variable from Poisson distribution minus its mean?

Given a random variable $Y$ from $\operatorname{Poisson}(λ)$ I am trying to understand what the distribution of $Y-λ$ is. I tried writing out the PMF of $Y-λ$ and obtained: ${λ^{k+λ}e^{-λ}}/{(k+λ)!}$. ...
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RStudio help with calculating variability independent of the mean [closed]

I looked at the the R code here (How to compute Variability Independent of the Mean (VIM)) but have run into my own trouble trying to calculate variability independent of the mean. I have included my ...
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How can I calculate and compare averages in a data set with different sample sizes?

I have a data set with about 1 million rows of data. The most important fields are the id, the date_time, the customer and the score. Firstly I want to calculate the mean score for each customer (...
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How sample mean and standard deviation (error) change if sample size is significant compared to population size (n>>0.05*N)?

How do sample mean and standard deviation (error) change if sample size is significant compared to population size? Things I Know So Far: If a population has a mean of $X$ and a standard deviation of ...
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2 votes
1 answer
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Adjust a Sample Mean towards the Population Mean

This feels incredibly basic but I can't seem to find the answer! Let's say I knew the pass rate for an exam in a huge population of students is 50% (let's say millions of students). A new class of N=...
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How to compare a mean with a mean of a means

For each patient, I have the value of a blood parameter on admission and several values of that blood parameter in subsequent days (not all the patients have the same number of posterior measurements)....
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How to calculate probability of true mean

So say I have a repeated measurement of subjects on a variable that has correlation of r=0.7 between within-subject measurements. I calculate the within-subject SD (=wSD) of the measurements with sqrt(...
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Regression on average values

Is it possible to do a regression on average values of categories? I have categories of function type, building year and surface (dummy variables of categories) and average values of energy ...
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Mean variance relationship

I am working on a dataset on time devoted to domestic work by individuals I have grouped the data based on the day of the week the information has been collected. This was done to examine the relation ...
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Best way to determine that two sets of sample means are not different (with 95% confidence)?

I am given the averages and standard deviations of two sets of data. The average is computed by running a non-specific optimization algorithm 30 times and averaging the result. I am trying to ...
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What is the phenomenon I'm observing here?

I was looking at the St. Petersburg paradox and wanted to make a quick simulation to see the results. I made a quick program simulating 1 Billion "games" and the average of the gain (over ...
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Is it fine to present Median and IQR for normally distributed data?

I have data with more than 25 variables. Some of them are normally distributed and others are not. Instead of checking each variables for normal distribution and presenting ...
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What to do when comparing mean of two populations and one is not normal?

I have a dataset with two populations (unpaired). First one with 36 observations, second one 74. The first passes the Shapiro normality test with p-value = 0.1521, ...
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How to deal with redundant data within a sample when calculating the standard error?

In my research, I analyse pixel data from a 2D microscope image. Each pixel represents a unique spatial position. In my image, each pixel $i$ has a corresponding brightness value $x_i$. I assume the ...
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Testing for constant mean (stationarity)

I have a grayscale digital image with noise and I would like to test for uniformity in small neighborhoods. One hypothesis says that the mean is independent of the spatial coordinates, against the ...
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Can we write mean $\mu$ for a given distribution in terms of RSS? Also standard deviation $\sigma$ in terms of RSS?

I am trying to express mean and standard distribution in terms of RSS so that I have a formula for likelihood in terms of RSS.
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2 votes
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Probability that interval arithmetic estimate of mean covers the true mean of a normal variable?

Background Suppose there exists a normal variable $X \sim \mathcal{N}(\mu, \sigma)$ where $\mu, \sigma$ are known. Also suppose that you only observe rounded instances $Y = \operatorname{round}(X, d)$ ...
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Lasso regression prediction on test set is predicting towards the mean of the train set?

I am using lasso regression to predict age (continuous data) from a set having 2112 numeric features (indepedent variable). The training dataset contains around 2773 participants. The mean of that ...
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Skewed distributions: choosing the median or average

Goal: To determine whether to use the median or average (or a weighted combination of the two) from a data set based on whether ...
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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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4 votes
2 answers
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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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1 answer
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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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