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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75 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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54 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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54 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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7 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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10 views

How do I determine the significance of a difference in weighted averages from a Likert-type survey question?

I have multiple survey questions that give respondents 4 Likert-type options for a response to qualify their knowledge/skill in a particular area. I have calculated a weighted average (and divided by ...
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172 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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10 views

Number of occurrences gives higher weights

I have this algorithm that I'm implementing that I need to change to give it a better accuracy. To give you an idea of the problem, I have a a bunch of lists that contain items and all items in these ...
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3answers
46 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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44 views

Paired test: many repetitions, few subjects

I have a situation similar to this: 9 normal-sighted subjects are each tested under two conditions: say, with and without spectacles (of a fixed power) and asked to reach towards an object many times ...
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53 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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80 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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25 views

how to use global weights to update local ones

I have a population of data points. Each data point expresses a different name. Each such name belongs to a different ethnicity, say {A, B, C, D, E}, with a probability. The sum of probabilities for a ...
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20k 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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18 views

How to use global weights when normalizing a mean value?

This is a very silly question, however, it confuses me a lot! Let's suppose that each observation consists of the prob of $A$ and the prob of $B$, with values $1/2$ and $1/2$ respectively. Also, ...
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35 views

Average difference in averages and t-test

I'm currently working with some individual level data and have run up against a wall in figuring out the best way to analyse it. Let me describe: We have a sample of N=9000 Physicians. For each ...
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17 views

Calculate scores for users with varying activity

I have a web application which allows users to take questions. Ultimately I store the following data: 1) Questions attempted by each user 2) Questions correct by each user 3) Avg. Time per user for ...
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24 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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24 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
200 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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19 views

League table with weighted result

I have a simple set of data indicating completion rates that I want to present as a ranked/league table. The data available is that for every visit of a person, a plan document should be completed by ...
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1answer
141 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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72 views

Averaging across independent strata: confidence interval

I've $k$ independent strata, with populations $n_1,\dots,n_k$, and have estimated the mean in each stratum $\bar{x_1}, \dots \bar{x_k}$ and obtained the standard errors $se_1,\dots,se_k$ (using STATA ...
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1answer
191 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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1answer
70 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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622 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 ...
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78 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 ...
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1answer
36 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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111 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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1k 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: ...
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633 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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1answer
81 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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889 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
129 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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140 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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111 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
131 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
143 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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1answer
254 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 ...
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195 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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179 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 ...
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1answer
2k 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 ...
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2answers
172 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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1k 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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241 views

Weighted harmonic mean vs weighted geometric mean [duplicate]

Possible Duplicate: Weighted geometric mean vs Weighted mean I searched for the differences between WHM and WGM. When to use each of them? when not?
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105 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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121 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
2k 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 ...
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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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425 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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194 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 ...