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Questions tagged [mean]

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

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5 vs 3 measurments of one parameter

Hellow, smart people of the internet, I have a question: We are doing a study of 170 people- where 20 parameters will be measured 3 times over 2years and the median of every parameter will be compared ...
Mila Bu's user avatar
3 votes
1 answer
228 views

Estimating mean and SD given the median and IQR values

it is possible to estimate mean and SD given the median and IQR? I am involved in a meta-analysis where some trials show outcomes as mean and standard deviation but most show median and inter-quantile ...
Stat2024's user avatar
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Non-parametric one-sample mean test for a bounded variable (based on Chebyshev's inequality?)

The problem I have $x_1, \ldots , x_n$ i.i.d. draws from r.v. $X$ such that $0 \leq X \leq 1$, but I can't make any other assumptions about the distribution. I want to test the null hypothesis that $E(...
Martin Modrák's user avatar
2 votes
1 answer
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Why can the standard error of the weighted mean be smaller than the standard errors of the individual measurements?

I am combining two independent measurements with their respective standard errors using a weighted mean. The measurements are: It seems counterintuitive to me that the standard error of the weighted ...
Francesco 's user avatar
4 votes
3 answers
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Why can't the slope be greater than 1 in regression to the mean for married couples' intelligence?

Consider the following example I read in Daniel Kahneman's book: Highly intelligent women tend to marry men who are less intelligent than they are. Kahneman argues that (slightly reworded for ...
MangoPizza's user avatar
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How to estimate the expected bin size "N" from "q" unique values among "p" draws, with replacement?

I have a set/bin/bucket containing an unknown N number of balls. Each elements ("balls") are assumed to have the same probability of being picked up. I ...
Jean Lescut's user avatar
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1 answer
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Variance around true value, not mean

The water temperature is 19 C, which is true value. I have measured the temperature of the water and I received such results: 18.7, 18.8, 19.1, 18.8. Can I calculate variance here around true value (...
Max Heron's user avatar
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Generate weighted median from activity per timespan

I have a set of data where I have a number of observations over the course of a year per individual. Generally speaking, I want to know the average activeness of the individuals that participated in ...
P.Weyh's user avatar
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6 votes
2 answers
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Calculate mu and sigma of a log normal distribution from p50 and p99 in javascript

I'd like to generate realistic sample data in javascript for monetary donations. I've chosen to model them as following the log normal distribution. I think a fairly intuitive way for a lay person to ...
michaelmcandrew's user avatar
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Does the mean of the maxima of a set of distributions converge?

This question is related to a recent one I posted. In that question I ask what statistic might best represent the central tendency of the true discrete distribution of a property for a sample for ...
Buck Thorn's user avatar
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1 answer
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How do I calculate estimated variance for an ensemble forecast?

I have several (n) different forecasts of comparable quality for a variable, based on the same data but using wildly different statistical models. For each, I have generated an estimate for m periods ...
andrewH's user avatar
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Question about replicates at different levels in a t-test

I'm a biotechnology master student. For an experiment, we wanted to know if there is a difference in the amount of bacteria grown at a certain temperature between two samples. So the setup is as ...
jacala's user avatar
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Calculating the mean and standard deviation from a normal distribution [duplicate]

I am interested in methods for finding the mean and standard deviation of a normal distribution. It is inspired by the following question that is part of the A-level maths course in England. The ...
Bysshed's user avatar
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Mean of weekly data smoothed with a 3-week moving average

I have weekly Influenza data for 6 years and I want to find the mean to plot over time so that I can compare to the weekly data for 2024 so far (here is the dataset). The problem I have is that the ...
R Maharaj's user avatar
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Comparing two populations mortality rates

I’m starting a report for open uni and am proposing to compare the mortality rates of cardiovascular disease between two countries. One is higher than the other looking at the data and I’m going to ...
Jason Kimmings's user avatar
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How to do average percentage based on two samples of three variables?

I have data like this case total_paths prev_val new_val 1 14 0 14 2 20 0 9 I need to calculate the percentage increment in the new value in average based on these two cases. For example, for case ...
Shyamkkhadka's user avatar
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Expectation of the product of two random variables

I recently tried to derive a formula that I saw in a paper. The scenario was a follows: Let $X\in\lbrace 0,1\rbrace $ a.s. be a binary random variable and $Y$ be a continuous random variable. Let $a,b\...
stats19's user avatar
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Is there an easy way to mentally calculate mean an variance? [closed]

Giving a generic numerical data is there an easy way to calculate mean an variance mentally or at least some easy formula that minimize the error with the correct mean and variance?
pgiacome's user avatar
4 votes
2 answers
121 views

Confidence interval for the sum of 2 binomially distributed variables

$P_1$ and $P_2$ are uncorrelated, binomially distributed variables with success probabilities $p_1 \neq p_2$. Say I measure: $k_1 = 9$ successes out of $n_1 = 10$ trials for $P_1$ and $k_2 = 1000$ ...
dimitsev's user avatar
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1 answer
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$\mathbb{E}[X^2]\leq k \mathbb{E}[X]^2$, upper bound second moment from first moment

Let $X$ be a non-negative random variable bounded on $[0,1]$. Is it true that $\mathbb{E}[X^2]\leq k \mathbb{E}[X]^2$ for some constant $k$? If not, are there any minimal assumptions on $X$ where this ...
ryanriess's user avatar
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1 vote
1 answer
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Conditional and unconditional mean in GARCH(1,1) model

Say I have a stationary time series and want to fit a GARCH(1,1) model. Does this mean that the conditional mean, which is used in GARCH, would always be the same as the unconditional mean of the ...
statwoman's user avatar
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Can raw means and estimated marginal means be the same ? And when?

I have read a lot about calculating raw (standard) means and EMM. First are data based (descriptive stats), the latter are model based. I try to learn how to calculate both of them. In my example both ...
Andrzej Andrzej's user avatar
2 votes
0 answers
62 views

Decision theory when distributions don't have a first moment? [closed]

Lets say that we are presented with two gambling opportunities and would like to decide between them in a decision-theoretic framework. For gamble 1, the cost is $1$ and the payoff is $X_1$ where $X_1 ...
QMath's user avatar
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3 answers
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How to estimate mean and standard deviation of individual result given a sample of batch results?

I apologize in advance if my title is not well-worded, or if I am using the wrong tags; this is my first time asking a question here. I want to analyze how long it takes for a system in production to ...
user10931326's user avatar
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Converting the unit for mean and standard deviation

I have a problem and it's been days and I couldn't find a solution Simply what I want to do for the purpose of a research data, I have the mean and standard deviation of some measurements in diameter ...
Ibrahim Hassan's user avatar
1 vote
0 answers
82 views

Standard Deviation and Standard Mean Error of measurement with uncertainties

It is well known that, given a set of $n$ values $Y_1, \cdots, Y_n$, its Sample Standard Deviation is $\sigma = \sqrt{\dfrac{1}{n-1}\sum_{i=1}^n (X_i - \bar{X})}$ and its Standard Mean Error is $\...
Bml's user avatar
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Why is taking the mean RMSE sometimes so far off overall RMSE?

I'm working with a multi-threaded program, which splits a dataset into N chunks, and evaluates some regression model's performance, predicting a score for each item in each chunk. I'm using RMSD as ...
Seán Healy's user avatar
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41 views

compare means of lognormal distribution

I have a small set of data that I used to generated a lognormal distribution: ...
efz's user avatar
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Can I compare two estimates by their sample variance?

For example, to estimate the population mean $\mu$, I am given two sample mean $\bar{x}_1$ and $\bar{x}_2$ from two (independent) data sets of $N_1$ and $N_2$ observations respectively. Without access ...
Rokai's user avatar
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1 vote
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Meaning of subscript $n$ in sample mean variable

I am reading Wasserman's All of Statistics. In Chapter 13: Linear and Logistic Regression, when deriving the least square estimates for simple linear regression, we have the data $(Y_1, X_1), \dots,(...
Ouroboroski's user avatar
11 votes
1 answer
961 views

Deviation between Mean and Median

If I have a mean of 15 and median of 10, is there a term for the difference between these? Can you use this difference of 5 for anything valuable statistically?
greenguy's user avatar
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1 vote
0 answers
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Calculating the mean of different SMRs

I have the SMRs of different local areas. The same reference population was used for the standardization. The local areas were divided into 5 groups (group1, group2,...,group5). I want to know if the ...
Luke's user avatar
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1 vote
2 answers
50 views

Calculated spread and mean using mean results only

Background: We have a large database of measurement data. The individual data points are actually the mean results of a particular sampling. No further information is available against each data point,...
JasonL's user avatar
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2 votes
1 answer
54 views

What is the intuition behind the single-pass algorithm (Welford's method) for the corrected sum of squares?

The corrected sum of squares is the sum of squares of the deviations of a set of values about its mean. $$ S = \sum_{i=1}^k\space\space(x_i - \bar x)^2 $$ We can calculate the mean in a streaming ...
Foobar's user avatar
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0 answers
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Estimating Standard Error of the Mean Across Multiple Samples: Method Selection and Best Practices

I have multiple samples, each of size (n), and I'm exploring different methods to estimate the Standard Error (SE) of the mean. I understand there are several approaches, but I'm seeking insights into ...
Catfoxes's user avatar
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71 views

Why regarding mean Average Precision for 50 and for 50 to 95? And can you average different evaluations?

I saw a lot of papers using mAP@50 and mAP0:5:95, but in terms of deciding how precise a trained object detection model is, I do not understand why often both values are discussed and shown. Wouldn't ...
Taka Incur's user avatar
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0 answers
41 views

Average of Percents, or Sum Total / Sum Total?

I have some data and need to know the average commission of all the items. For each row, I calculate the percent of items sent out. If I wanted to know, "What is the average commission", ...
BruceWayne's user avatar
1 vote
2 answers
94 views

Covariance of Best Linear Unbiased Estimators and arbitrary LUE

I'm working on a problem involving two linear unbiased estimators $T$ and $T'$ of a parameter $\theta$, defined from a sample $\{X_1, \dots, X_n\}$ with mean $\theta$ and finite variance. I aim to ...
Taha Rhaouti's user avatar
0 votes
1 answer
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K means clustering of image with k=1 vs mean of all pixels

I have relatively uniformly colored images and I extracted colors using k-means. k means 1 showed the best results for my modeling purposes, k means 2 not so much, and with k-means 3 there ceased to ...
phil27's user avatar
  • 1
3 votes
2 answers
204 views

Calculating $E[(\sum X_i)^4]$

Trying to figure where I'm going wrong with the following. My goal is to calculate var$(\bar X_n^2)$ using $E[(\bar X_n)^4]=\frac{1}{n^4}E[(\sum X_i)^4]$ given that $X_1,...X_n$ are iid with $EX_1=\mu,...
reyna's user avatar
  • 385
2 votes
0 answers
39 views

Confirming my calculation of mean, standard deviation and median for a histogram

Average travel time* for men = 27.2 minutes, women = 23.6 minutes My calculations are the followings: The problem is my calculated mean is 28.4 but chart says 27.2 I calculate the mean with this ...
Amir's user avatar
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2 votes
1 answer
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Can ANOVAs or Student tests be conducted on any summary statistic at the individual level?

I am wondering if ANOVAs or Student tests can be performed on any summary statistic of performance at the individual level without any effect on type 1 and type 2 error. For example, consider a simple ...
user1363251's user avatar
4 votes
2 answers
83 views

In R, why are the results of summary(lm(y~-1))$sigma^2 and mean(y^2) same?

Consider the following data and the model: y <- c(9,3,-2,7,6,12) lm(y~-1) summary(lm(y~-1))$sigma^2 [1] 53.83333 I expected ...
user232597's user avatar
0 votes
1 answer
39 views

How does a Random Sample relate to Random Processes and Random Variables?

What is the difference between a Random Sample, Random Variable (RV) and Random Process (RP)? As far as I know, a RV is a mapping from an experimental space to the real numbers and a RP is a mapping ...
Ahsan Yousaf's user avatar
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0 answers
11 views

Comparing ratios of independent means by calculating SE difference – applicable?

I am conducting a study comparing the ratio of a mean number of vocalizations to the mean number of individuals across three treatments. For each treatment, I have the mean number of vocalizations (...
Yael Lehnardt's user avatar
1 vote
0 answers
22 views

General Expression for the $t$-th difference of conditional means

In econometrics, it is common to work with the difference-in-differences of conditional means. For example, let $Y$ denote a variable of interest and $X_{1}$ and $X_{2}$ denote binary regressors. The ...
Kevin Durant's user avatar
5 votes
1 answer
158 views

What do I do when I *want* to accept the usual null hypothesis?

I have samples from two random variables, and I'm assuming normal distribution with equal variance. I want to show that the distributions have equal means $\mu_1$ and $\mu_2$. The usual two-tailed t-...
kdbanman's user avatar
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3 votes
0 answers
56 views

Is this ratio between sum of squares beta distributed?

Consider $x_i \sim N(\mu,\sigma)$ I am interested in distribution of the the following statistic (arises from likelyhood ratio test): $$ \frac{ \sum_{n=1}^{n} (x_i - \overline{x})^2 }{ \sum_{n=1}^{n} (...
Bait Hoven's user avatar
1 vote
1 answer
43 views

Box plots of monthly averaged water flow

I am working with a model that models water flows in a certain area. These flows can be influenced by taking certain measures, resulting in multiple water management scenarios. I would like to compare ...
Nathan's user avatar
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0 votes
0 answers
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Gaussian posterior/posterior predictive mean [duplicate]

I'm a little confused regarding the difference between the posterior and the posterior predictive distribution. I know that the posterior is a distribution over the parameter, while the posterior ...
Jannik's user avatar
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