A weighted mean (or weighted average) is like an ordinary mean, but the observations don't contribute equally - more emphasis is placed on some data values than others; they are weighted by a bigger or smaller amount than 1/n.

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119 views

Averaging standard deviations of unequal weight?

I'm sorry if the title is unclear, but I'm not sure of the appropriate way to phrase this question. I'm in med school (and sadly not as versed in statistics as I ought to be), and I am trying to use ...
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1answer
17 views

I get a different result when I try and calculate the mean-variance formula of risky and riskless asset [closed]

I'm having trouble seeing how the expected return of a two asset portfolio, where the weight of the risk-free asset is positive, but the weight of the risky asset is negative, results in the final ...
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50 views

Construct confidence interval for price per area, from weighted average price for quantity, and weighted average quantity per area

I have function for obtaining the weighted mean for price per quantity, where $p$ is price, and $w$ is the weight, for some product $i$. $$\bar p_a = \sum p_{i} w_{i}$$ and a quantity per area, ...
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2answers
73 views

How should I determine an average from a set of averages

I have a set of lines. I measure their length each 5 times, and then take the mean of their lengths (as I measure them). I also take the standard deviation. I want to know the 'average' line length. ...
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213 views

Standard Error for Relative Frequency Distribution

I have a weighted distribution with weights $w_i$, such that: $$\sum_i{{w_i}}=1$$ I know that the mean is defined by: $$\sum_i{{w_i}{x_i}}=\mu$$ And that the unbiased variance is defined as: $${\sigma}...
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243 views

Borda Count (Weighted Sum) vs Weighted Mean

I recently ran a survey where I gave users 36 options and had them rank their top 10 from most important to least important. I've taken the results and assigned each position a weight (i.e. ranked ...
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190 views

Identification of Difference in Weighted Mean and its Standard Error in Clustered Data Using Stata

I already asked this question on the statalist but have not received any comments on this issue yet. So I am going to post it here too. I am concerned with the following problem. Suppose my data ...
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2answers
156 views

Will the mean of a set of means always be the same as the mean obtained from the entire set of raw data?

If I have calculated the mean for 4 data sets (which do have different sample sizes), can I then obtain an "overall mean" by calculating the "mean of the means"? If yes, will this "mean of the means" ...
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44 views

Do I need to use weighted means with the Wilcoxon signed rank test?

I have 22 patients. They have been measured pre and post treatment. There are 3 measurements per patient before treatment (pre baseline), and four measurements after treatment (post baseline). There ...
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95 views

How did they do this analysis? (weighted proportions)

I've read with interest the report by Ayanian et al "Racial and Ethnic Disparities among Enrollees in Medicare Advantage Plans" [1]. They have estimated adjusted proportions of individuals that ...
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69 views

Computation of the entropy of marginals?

I have implemented this paper: Efficient graph-based semi-supervised learning of structured tagging models In the last sentence of the section 4.2, the authors have mentioned another possible way of ...
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1answer
71 views

Obtain adjusted means - Weight? Standardize? Use LSmeans?

I'm attempting to compare means from one year to another (and between groups at the same time point) by calculating adjusted values. I'm not sure what method to use. I've thought about the following: ...
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54 views

Mean of an interval censored random variable

It is likely that I am incorrect terminology here, but I am trying to compute a "mean" of an interval censored random variable. Here is an example where: 1. a random sample from the standard normal ...
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1answer
31 views

Representing a subset of observation using weights

I have $n$ observations for $m$ variables that are sorted by time, e.g. observation $1$ is the oldest, whereas observation $n$ is the newest. I represent this data as an $n\times m$-dimensional matrix ...
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47 views

with two EWMA means of different window sizes, can we estimate any other means? slopes? jumps?

EWMA is defined as follows(1, 2, 3, 4, 5): $$ \mu_{N} = \frac {1}{N} \Sigma_{i=1}^{N}x_i $$ $$ =\frac {1}{N} \Sigma_{i=1}^{N-1}x_i + \frac{1}{N}x_{N} $$ $$ =\frac {N-1}{N} \frac{1}{N-1} \Sigma_{i=1}^{...
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175 views

Aggregating Standard Errors for Predicted Probability Estimates

I obtain predicted values from a logistic regression for a certain outcome (e.g., mortality) at the hospital level – the data is at the patient level – and need to compute the average across hospitals....
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177 views

Exponentially Weighing Moving Average (EWMA) for weekly data

I'm aware that the typical EWMA approach is applied over larger time periods (say for Volatility, where lambda = 94% and all weights add up to 100% for stock returns data from last 5 years). ...
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145 views

Weighted variance of the weighted variance in frequency transition matrix?

Assume I have a $m\times n$ Transition Matrix $A$ with $m$ different observations and $n$ represents a discrete state space. Each column counts the frequency that state $j\in [1...n]$ was visited from ...
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1answer
228 views

Inverse-variance weighting

I'm writing a Bachelor Thesis in engineering an a small part of it has two deal with assigning weights to independent measurements. This is from the thesis: I am pretty sure that what equations (3....
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1answer
33 views

Estimating costs with extreme values

I am trying to estimate health care costs and I was wondering what the standard practice is for extreme values? By extreme values I mean I have a large portion of my costs being zero and a small ...
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75 views

Weighting on tables

I have a question about terminology. Suppose I have data categorized by three factors A, B, and C, with cell means $\bar{y}_{ijk}$ and cell frequencies $n_{ijk}$, where $i$, $j$, and $k$ index A, B, ...
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1answer
36 views

Appropriate weighting for averages

What is the appropriate (or the advantages of disadvantages for each) measure for weighting mortality rates across countries: total population or total number of deaths? For example, if you have age-...
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1answer
255 views

Calculating and comparing weighted means with changing number of daily values

I have daily data where the number of values changes with each day. I would like to calculate the weighted mean of this data, where days with more values are weighted higher than days with less. ...
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1answer
400 views

Compare Log-Normal Distributions

I am looking at distributions for the fuel consumption of vehicles in the US and I have two sets of data: Data Set 1 - This is a dataset for the fuel consumption of all vehicles made available for ...
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1answer
464 views

Estimating an overall summary statistic (mean) for a value reported by ten published studies

Background I am writing a systematic review and meta-analysis of the association of exposure to X with the outcome Y. I have identified ten studies that report on this subject. This will be a meta-...
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1answer
118 views

How to compare subjects with different weights?

I have a collection of products that could be rated as good or bad. Every product has a grade, that is the sum of "good" votes minus the sum of "bad" votes. These products are also split into two ...
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32 views

Computationally cheap estimation of the mode from 2D samples

I say 'mode' in the title – perhaps there's something more appropriate I can find. Here's my problem: A person is in a $100\mathrm m$ by $500\mathrm m$ space. I have about 100 samples randomly ...
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3answers
141 views

How to calculate the weighted mean?

For example assume I have three observations as given in matrix A $A = \left[ \begin{array}{ccc} 1 & 0 & 1 \\ 1 & 1 & 0 \\ 0 & 1 & 1 \\ \end{array} \right]$ each row vector ...
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1answer
282 views

Weighted average of measurements with unequal errors

Suppose I have the numbers below. Consider them as results of some measurement. 22.73 +2.15 -1.81 23.81 +1.77 -1.54 28.6 +11.4 -6.4 29.59 +8.58 -5.43 ...
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1answer
826 views

Standard deviations and confidence intervals (weighted) running average

My question is related to this one. I am calculating averages, actually as many as I have samples because I calculate a running average, and for equal weighting I know how to calculate the $95\%$ CI, ...
2
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310 views

Weighted Standard Deviation vs. Weighted Regression Standard Error

This is an R question. I have $n$ observations of the variable $y$, with each observation, $i$, weighted by $w(i)$. Each $w(i)$ weight falls between zero and 1, with the sum of the weights, $m<n$....
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39 views

Aggregating based on inverse probability weight

I have a data set that includes life quality indices for many cities. I want to aggregate the indices to the metropolitan level. Since some cities in each metro area are missing, the data set provides ...
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51 views

How do I determine the appropriate “weight” of a point in fantasy basketball?

For fantasy basketball, I want to quantify a player's output based on his Points, Rebounds, Assists, Steals, 3s, and Blocks production. Let's pretend that over the course of an imaginary basketball ...
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1answer
964 views

Degrees of freedom for a weighted average

And yet another for the long list of degrees-of-freedom questions! Given an i.i.d. sample $x_1,..., x_n$ from an arbitrary real-valued distribution with expectation $\mu$, the sample mean can be ...
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1answer
1k views

Using the eigenvalues from PCA in k-nearest-neighbours

I'm quite new to this StackExchange, only been a lurker till now, but my StackOverflow fellows have said you'd be the best people to ask about this. Anyway, enough introduction. I'm using the ...
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1answer
173 views

Comparing two lists to measure for similarity

The problem I am trying to solve is finding the probability that two people are the same by cross-referencing the associates of the two people. For example, if person A is associated with the ...
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87 views

How to bootstrap confidence of a weighted measure?

I have a large data set of 20M observations with 20+ measures for each observation (people). Additionally I have a set of weights that reflect the racial population where each person lives. For ...
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3answers
2k views

Weighted standard deviation of average

For two groups (a and b) with unequal numbers of observations (n=10 and n=30), I have given their means and sd. Calculating the weighted mean is pretty straight forward. But how can I derive the sd of ...
5
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1answer
169 views

Standard error of a weighted mean when observations are not independent

I have a situation where I have a bunch of noisy observations with known (and normal) sampling error and a non-trivial co-variance structure between the observations. In an uncorrelated setting, I'd ...
2
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1answer
65 views

Estimate the parameters of an ellipse in the presence of large outliers

I have a number of points $x_1,\ldots,x_m\in\mathbb{R}^n$ with weights $w_1,\ldots,w_m$ between 0 and 1. There is an ellipse which contains a very high concentration of points with weights close to ...
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2answers
4k views

How to compute weighted means and SDs?

I want to calculate volume weighted average price and standard deviation for the following dataset: ...
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2answers
350 views

Confusion regarding weighted average

This is a pretty simple question and I'm wondering how to go about finding a solution. I have the following data. ...
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1answer
187 views

Given weighted mean and raw data, derive weights to minimize error

Imagine I have a set of data from an experiment: Observed Measurement 1: 5 Observed Measurement 2: 6 Observed Measurement 3: 7 Observed Measurement 4: 8 Observed Measurement 5: 9 I have a target ...
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1answer
12k views

Weighted Variance, one more time

Unbiased weighted variance was already addressed here and elsewhere but there still seems to be a surprising amount of confusion. There appears to be a consensus toward the formula presented in the ...
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137 views

Best fit of weighted mean?

The title might be somewhat misleading. I am trying to solve the following optimization problem and do not find any clues. Can any one help? I have a sequence of $n$ observation $s_i$. Each ...
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1answer
325 views

Is there a more elegent solution for exponentially weighted-mean in R? [closed]

OK so I have a working code to do what I want but I am new to R and feel like my solution is very clunky and there is likely a more efficient way to get the same result. I have a set of data that ...
2
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1answer
166 views

Computing lowess mean value

I am trying to reimplement the lowess algorithm in java. I read the matlab page explaining lowess with the following steps: Compute the regression weights for each data point in the span. A ...
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1answer
398 views

How does a Daniell kernel differ from a two sided average?

As far as I can understand, the Daniell kernel, is simply $K(j/M)=\frac{1}{2M+1}1(|j|\leq M)$. Namely, this is a two sided average. Why do people call this an untruncated kernel and differentiate ...
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2answers
191 views

How to solve this “probabilities and weighted probabilities” type of question?

I always get confused by "probabilities and weighted probabilities" type of questions as I can't differentiate between the two of them. Consider following example. Urn 1 contains 5 white balls and ...
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2answers
3k views

Bias correction in weighted variance

For unweighted variance $$\text{Var}(X):=\frac{1}{n}\sum_i(x_i - \mu)^2$$ there exists the bias corrected sample variance, when the mean was estimated from the same data: $$\text{Var}(X):=\frac{1}{n-1}...