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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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: ...
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1answer
514 views

Determining true mean from noisy observations

I have a large set of data points of the form (mean, stdev). I wish to reduce this to a single (better) mean, and a (hopefully) smaller standard deviation. Clearly I could simply compute $\frac{\sum ...
9
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1answer
182 views

Voting system that uses confidence for each voter

Let's say, we have simple "yes/no" question that we want to know answer to. And there are N people "voting" for correct answer. Every voter has a history - list of 1's and 0's, showing whether they ...
8
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1answer
266 views

Averages of averages (of averages, of averages…)

Consider the following cell biology experiment. We are comparing $T$ different treatments of cultured cells. Each treatment $t$ is replicated in several (microtiter) wells, indexed by the variable ...
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24k views

How do I calculate a weighted standard deviation? In Excel?

So, I have a data set of percentages like so: ...
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3k views

Computing standard error in weighted mean estimation

Suppose that $w_1,w_2,\ldots,w_n$ and $x_1,x_2,...,x_n$ are each drawn i.i.d. from some distributions, with $w_i$ independent of $x_i$. The $w_i$ are strictly positive. You observe all the $w_i$, but ...
4
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1answer
272 views

Estimate the population variance from a set of means

I have a set of measurements which is partitioned into M partitions. However, I only have the partition sizes $N_i$ and the means $\bar{x}_i$ from each partition. Because all measurements are assumed ...
4
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3answers
779 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 ...
4
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1answer
3k views

A simpler way to calculate Exponentially Weighted Moving Average?

Proposed Method: Given a time series $x_i$, I want to compute a weighted moving average with an averaging window of $N$ points, where the weightings favour more recent values over older values. In ...
4
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1answer
204 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 ...
4
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1answer
89 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 ...
4
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1answer
501 views

Negative weights in a moving average?

A number of well known moving averages, such as Spencer's 15 point MA, and Henderson moving averages have negative weights in the averages. What does this mean in a conceptual sense? What information ...
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53 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
185 views

How do I introduce features and their confidence values into classifiers

I would appreciate some advice on how best to weight or give more importance to a percentage with a larger denominator. Eg A. 1 out of 2 = 50% B. 5 out of 10 = 50% C. 500 out of 1000 = 50% Some of ...
3
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1answer
53 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. ...
3
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1answer
323 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 ...
3
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2answers
2k views

Weighted geometric mean vs weighted mean

I have a set of data, each element has a weight. I need to estimate the mean of this data. I found that there are two ways: A weighted geometric mean and a weighted mean. When should I use each of ...
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1answer
1k 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 ...
2
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1answer
80 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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1answer
88 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 ...
2
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1answer
189 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 ...
2
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3answers
65 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 ...
2
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1answer
194 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, ...
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1answer
39 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
617 views

Weighted mean of two 2D Gaussian random variables

I have two 2D Gaussian random variables. I'd like to find the weighted average of the two (based on their covariance matrix around the mean, meaning that the mean of the final Gaussian should be ...
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0answers
153 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, ...
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57 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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31 views

Estimated Treatment Effect in the full sample is not between the estimates of the stratified samples?

I am estimating the relationship between students' math scores and using a supplemental math software. I've adjusted for some demographic variables in the model. In my first model, I use the full ...
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0answers
34 views

How to symmetrically adjust data by removing certain value

Say I have a data set in the following format: {a:200, b: 100; c:400} The sum of a, b and c equals 700. Now, I have another value which is supposed to be the actual total say 500. How do I adjust ...
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139 views

Always get confused by “probabilities and weighted probabilities” type of questions as cant differentiate between two

Urn 1 contains 5 white balls and 7 black balls. Urn 2 contains 3 whites and 12 black. A fair coin is flipped; if it is Heads, a ball is drawn from Urn 1, and if it is Tails, a ball is drawn from Urn ...
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2answers
204 views

Better method to estimate gender gap: difference between medians or median gap by occupation?

I'm doing some analysis of Bureau of Labor Statistics data on wages earned by men and women, and I'm trying to determine which of the two methods I've used is the better estimate of the gender wage ...
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2answers
1k 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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1answer
50 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 ...
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1answer
174 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 ...
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1answer
282 views

How to relate raw scores on five-point Likert to three conceptual categories?

My thesis is on employee productivity and I had a questionnaire which consists of a five-point Likert scale (5-strongly agree, 4-agree, 3-agree, 2-disagree, and 1-strongly disagree). On the other ...
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2answers
242 views

How do I calculate the ranking of some galleries based on the rankings of the artists represented by them?

The mean is not good in this case, because there are galleries that have an artist with a high rank and several other artists with way lower ranks. I'm thinking about doing a weighted mean, but I ...
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1answer
21 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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1answer
98 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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1answer
107 views

Error on weighted mean

I have some measured datapoints. Each of the points has attached an error, depending on how precise the measurement was done. Now I'm using the squared weighted mean with the inverse of the errors as ...
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1answer
75 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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19 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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1answer
115 views

Weighted average of measurements with unequal errors

Suppose I have the numbers below. Consider them as results of some measurement. ...
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0answers
26 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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0answers
32 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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0answers
137 views

Hypothesis test for difference between domain means with weighted data

I have a large dataset that is weighted due to: probability proportional to size sampling, & disproportionate stratification. I would like to compare the means for two different domains ...
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2answers
182 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. ...
0
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1answer
126 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 ...
0
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1answer
293 views

Optimize Weights used in a Weighted Average

I want to calculate a weighted average, mostly for illustration purposes. However, I have an outcome variable that is Y/N and would like to optimize the weights relative to this outcome. What are ...
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1answer
201 views

Handling missing attributes when using weighted average

I was trying this optimization where I have some predictors and I want to predict the real value using weighted average of the predictors. What I am trying to do is given the predictors' prediction ...
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1answer
299 views

Standard error for the sum of weighted means

I am looking at a two-stage process of diagnosis. Stage 1 is a screen that identifies people with the diagnosis with some error, Stage 2 is a detailed examination (a gold standard) In Stage 1, N ...