Questions tagged [mean]

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

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20 views

How to calculate mean and SD between $T_1$ and $T_2$ based on mean and SD from $T_0$ to $T_1$ and $T_0$ to $T_2$?

I am performing a meta-review about the transition of control in semi-automated cars, for which I am trying to retrieve specific means and standard deviations. I am not sure if I am using the right ...
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How can I shift the average probability keeping constraint (0.0:1.0)?

I have a large datasets of values that range from 0 to n. I am interpreting the values as probabilities for a later pseudo-random selection process. To make the values serve as probabilities, I ...
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Significant T-test with small mean difference but large standard deviation

I have recently run some analyses to test whether those participants lost to follow up are significantly different from those who stayed in the study. N= 590 for those who stayed and N=258 for those ...
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Sampling distribution of the mean of the discrete-power law distribution

For a certain problem I wish to generate random integers $k$ so that their distribution follows $p_k \sim k^{-\alpha}$ for $k \geq k_{\text{min}}$, $k_{\text{min}} > 0$. I am following the ...
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Where does the expected value definition come from? [duplicate]

The definition of the expected value on the domain $[a,b]$ is given by $$E[X] := \int_a^b x f(x) \, \mathrm dx $$ I understand what the mean is, but I don't fully understand how this specific equation ...
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What is the expectation of absolute difference

Given: E(|X-R|) =2.5 E(|L-X|)= 3 where X, R, L are assumed to be normally distributed and independent. Standard deviations of |X-R| and |L-X| are known. what is E(|L-R|) ?
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giving the sample covariance formula I want to show that they are equal [closed]

I want to understand how to move from the first formula of sample covariance in the image attached to the one below as indicated by the arrow
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1answer
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Standard Error of the Mean: Do I use the main dataset's SD, or the sample's SD?

There's a nationwide dataset of the average scores on test, by school (each school has one entry in the dataset). There are significant differences between the means and SDs among the states. A subset ...
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Probability of a sample mean higher than population mean

I have solved this question but I am not sure if what I did is correct: It is found that the population mean and standard deviation for the paper are 45.292 and 18.761 respectively. Find the ...
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Is it valid to compute the Spearman rank correlation's p-value on summarized (mean/median) data?

I have a dataset generated as follows: On each day for 30 days, a measurement is made for each individual. Individuals are separated into two groups. Each group contains 5 individuals. Is it valid to ...
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variance of theoretical mean of y at given value of x in regression [duplicate]

Could someone tell me where I might find information on deriving the standard error used in confidence and prediction intervals of y at a given value of x on a regression line. I can't find anything ...
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Can I log-transform the sample variance estimated from an originally log-transformed data?

I have a dataset that is log-transformed to meet the assumptions of normality. I have estimated the mean and variance of each individual. I understand that the obtained mean is log-transformed. My ...
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Combined Variance through Several Linear Functions

Apologies in advance if my terminology isn't correct for everything I'm about to write I am dealing with a corner-cased problem and I'm trying to figure out if my derivation is correct. I have a large ...
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What is the difference between using SDs away from the mean and SEs away from the expected value?

I've always learned about the bell curve concept as having units in SDs away from the mean. For example, if the mean is 5 and the SD is 2, then the curve is centered around 5, and, for example, a data ...
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How to separate the relationship between mean and standard deviation, mean and coefficient of variation?

I have again a similar question related to my previous posts. Please consider the following scenario: Mean and standard deviation of A are positively correlated. Mean and coefficient of variation (CV)...
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Calculate minimum detectable effect

I need to calculate analytically the minimum detectable effect when comparing two-sided 2 sample proportions z-test for given sample size (different sample size per group), significance level and Type ...
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How to calculate the mean and standard deviation of combined series?

A company produces two products. It sells the product P1 per month and the product P2 per season. The revenue of the product P1 over one year (with monthly frequency) is stored in A. ...
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Effect of nonlinear transformations on the mean

Suppose I have a continuous random variable $X$ and a random variable $Z = f(X)$, where $f$ is a nonlinear monotonic transformation. How can I prove the following relation between the mean and the ...
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Distribution where mean and mean of reciprocal are both 1 [duplicate]

Is there a non-trivial distribution for a positive r.v. $X$ such that $\mathbb{E}(X) = \mathbb{E}\left(\frac{1}{X}\right) = 1$? If possible, I'd like the distribution to support (have positive ...
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Sample size required for a given margin of error in sample mean when population standard deviation is not known

I have trained a regressor to predict the revenue generated when users click on an ad impression. Only few clicks eventually lead to positive revenue. As such, I have used the Tweedie regression in ...
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Is estimation of Coefficient of variation (CV) misleading when sample mean and standard deviation is negatively correlated?

I have a dataset with 145 individuals and two traits measured in 12 environments. I want to measure the variation among individuals i.e. individuals with high performance in one environment and low ...
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How to interpret results of survey with more options to select and find mean, median, modus

From mini-survey of 8 system users was found that: 1 Uses website 4 iPhone app 7 Facebook 2 Twitter 2 E-mail subscription 1 user can use more communication platforms. How can I say: “From this ...
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The quantile of prob=0.05 and mean

What is the meaning of the difference between the quantile of prob=0.05 and mean for a sample form a specific distribution? In other words, I would like to understand the relationship between ...
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Can I use the sample mean to check whether non-normally distributed populations are different?

I've run a user-test of a tool where 86 users participated and scored the a according to the System Usability Scale. The scale goes from 0-100, with 0 being the worst and 100 being the best. The ...
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Should I use 'median' instead of 'mean' for nonparametric distributions?

I have a dataset that I determined was nonparametric. If I want to do calculations like '% change', and find the average percentage change, should I really find the median percentage change instead of ...
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I want the mean of a group of means where some instances have multiple means. Should I include all scores, or only one mean per instance?

I have a list of mean usability scores for different tools. Some of these tools have been tested separate times, giving different scores. I now want the mean score for the entire group of tools - what ...
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How to compare factor levels when more than one categorical variable is present?

I have 2 categorical variables in my data: g1 and g2. g1 has 5 levels:0,1,2,3,4. g2 has 2 levels:0,1. Below you see the coefficients and their errors and individual p-values and so on. I was wondering ...
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Telling which group's mean value is higher using lm()?

We have groups A,B,C and we try to see if their means are different. Below are the summary of the linear model fitted.Below you can see group A is the reference group.Can I say checking coefficient ...
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replacing nas when 50% or more of the data is missing

I have to perform a linear regression on a dataset. However, I am having trouble figuring out what type of imputation I should do on the data because in some cases the majority of the the data is ...
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Sampling distribution of sample means question (Newbold)

6.3 from Newbold (8th ed.): A population contains 6 million 0s and 4 million 1s. What is the approximate sampling distribution of the sample mean in each of the following cases? The sample size is n ...
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Calculating the Mean of an Ordinal Variable Question

I have distributed and analyzed a survey regarding teaching quality. For some of the questions, I ask how often a given teaching method is used. When doing this I ask them to select one of the ...
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How do you find the asymptotic distribution of a function of the sample mean?

There are a number of questions on this site that ask for the asymptotic distribution or moments of some function of the sample mean for IID data (see e.g., here, here, here, here and here). All ...
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Number of samples needed to estimate population mean to given margin of error

The population distribution is unknown, but is probably multi-modal. The required margin of error is given in advance. Any number of samples can be drawn from the population. Given enough samples, ...
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How to calculate an average from three distinct but related samples?

I am trying to find out how to average price information stemming from three different types of products belonging to three distinct groups: Red Cars, White Vehicles and Blue Vehicles. The information ...
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What are good methods to deal with outliers when calculating mean of data?

I have a dataframe with yearly energy uses of buildings over 5 years. In order to have a representative yearly energy use for data modelling, I'll have to take the mean of those data. As the data can ...
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170 views

How would you find the mean of the zero truncated Poisson distribution? [closed]

Given the probability mass function is, $f_T(y)=P(Y=y|Y>0)= \frac{1}{e^\lambda -1} \cdot \frac{\lambda^y}{y!}, y=1,2,3,\dots$ Where, $f(y)=\frac{e^{-\lambda}\lambda^y}{y!},y=0,1,..$ How would ...
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Proof that the mean of predicted values in OLS regression is equal to the mean of original values? [duplicate]

https://en.wikipedia.org/wiki/Pearson_correlation_coefficient#In_least_squares_regression_analysis I was reading this page and came across the fact that the mean of the predicted target values for an ...
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184 views

What can I say with mean, variance and standard deviation?

I wrote this code in R: ...
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What's the relationship between $\frac{1}{n}\sum_{i=1}f(X_{1i},X_{2i})$ and $\frac{1}{n^2}\sum_{i}\sum_{j}f(X_{1i},X_{2j})$?

Suppose $(X_1,X_2)$ is a bivariate random vector following distribution $G$. $f(x_1,x_2)$ is a known bivariate smooth function. Suppose we are interested in estimating $E[f(X_1,X_2)]$ using a random ...
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48 views

What estimation method establishes sample mean and sample variance as estimators of mean and variance?

Sample mean and sample variance can be derived as MLE estimators for the mean and variance of a normal distribution. For a distribution in general, what kind of estimation method leads to sample ...
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Relative Median Absolute Deviation

For example, the CV (coefficient of variation) is the relative standard deviation (sd divided by the mean). Now is there a relative MAD (Median absolute deviation https://en.wikipedia.org/wiki/...
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In a One-Way MANOVA, can one of the levels of the IV have a mean of 0 with a standard deviation of 0 on one of the dependent variables?

I realize that this sounds like a very stupid question, but I need to make sure—please stick with me. The project in question is a quantitative content analysis; for the sake of this example, let's ...
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Is there a name for the midpoint of a sum (not a mean or median)?

I have a set of purchases with $ values like this: {1, 1, 1, 2, 7, 8, 10, 10, 20, 20}. Sum: 80. Mean: 8. I had thought that if you split this into equal sums (of 40), this would occur at the mean (8)...
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Exhaustive list of techniques used to estimate population mean and variance?

In beginning stats, we were told that: $\bar{x}$ is an unbiased estimate of $\mu$ $\frac{1}{n - 1}\sum(x - \bar{x})^2$ is an unbiased estimate of $\sigma^2$ As I am reading more, I have learned that ...
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Does Bayesian statistics bypass the need for the sampling distribution?

Let's take the classic case where the population follows a normal distribution, observations are iid, and we want to estimate the mean of the population. In Frequentist stats, we calculate the ...
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Independent t-test for between 2 samples, using function other than Mean

I have 2 sample groups of n = 1000 individuals for each group. Each individual rates the quality of a product on a scale from 1 to 10, and these rating are the ...
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How to calculate therical `mean`,`sd` based on given distribution paramters in R?

Example: gamma distribution with shape=4,rate=0.05. Checked wikipedia,In ...
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20 views

How to approximate sample mean age of people in a survey from grouped data

I am trying to calculate the approximate mean age of people that participated in a survey. I have 4 age groups: $[0,15);\,[15,35);\,[35,55)$ and $[55,75).$ For each group age I have the number of ...
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How to calculate the threshold value for a variable

In a question-answer platform, in each week the platform releases a new question. In total there are 15 questions. There are these three types of users. Log in every week, and answer in the correct ...
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Mean of target values at different time points as predictor in multiple regression

I've received regression model that predicts crop yield based on data collected at 3 time points (years). Input data contains multiple attributes and crop yield in the given year for a given location....

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