Questions tagged [mean]

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

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Example of mean independent variables but dependent still

Econometric textbooks often make the distinction between three types of independence: Stochastic independence: $\mathrm{D}(u|x)=\mathrm{D}(u)$ Mean independence: $\mathrm{E}(u|x)=\mathrm{E}(u)$ ...
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Determine the Sampling Distribution [duplicate]

Let $X_1,…, X_n$ be a sample of $iid$ $N(𝜇, 𝜎^2)$ random variables. How do you calculate or determine the sampling distribution of $\overline{X} = \frac{1}{n}\sum\limits_{i=1}^n X_i$ and $S^2 = \...
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Any help with this statistic question is much appreciated! [closed]

I am having a little help with this stats question. Any help with this is much appreciated!!
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When we calculate mean and variance, do we assume data are normally distributed?

When we calculate mean and variance using the two equations taught in school: $\mu = \frac{1}{N}\sum_{i=1}^N{x_i}$ $\sigma^2 = \frac{1}{N}\sum_{i=1}^N{(x_i-\mu)^2}$ Then do we assume, that the data ...
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Explaining different results of linear regression compared to students t-test

I am looking for some literature about linear regression and students t-test to cite them in my discussion within my paper. In a nutshell: I would like to argue that I prefer using the results of a ...
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Superiority of linear regression compared to students t-test

I am looking for some literature about linear regression and students t-test to cite them in my discussion within my paper. In a nutshell: I would like to argue that I prefer using the results of a ...
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1answer
16 views

How do I know which way this sample is skewed?

I have a sample where n = 15 and the median = mean but the mode is less. So I know to be: Positively skewed (mode<median<mean) Negatively skewed (mean<median<mode) Symmetric (mean=median=...
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Test diffrances of means in zero inflated, non normal distribiution

I have a big number of clients, that can be either treated with and ad (target group) or no (control group). The purchases after set amount of days are drawn from zero inflated (>50% of zeros) ...
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How to analyse intra-individual difference between two situations, with unequal sample size for each individual?

The setup is like this: each individual is measured in each of two situations a measurement can yield zero or more usable results I want to answer the question: "Does the situation affect the ...
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Unstandardize z score values that have mu and standard deviation of 0 and 1 respectively

Is it possible for one to unstandardize z score values with mean 0 and standard deviation of 1 back to its original value, given that the mean and standard deviation of the original data is not ...
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Assigning weights to a list of averages when all I have is the mean, standard deviation, and number of samples

I have some data which, essentially, gives the change in value of a particular stock option according to 1 movement in price of the underlying stock value. For example, say stock 'ABC' has 4 different ...
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Sufficient Statistic for Variance (Normal Distribution)

Suppose $X_1, \dots, X_n \sim N(\mu, \sigma^2)$. If $\mu$ is known and $\sigma^2$ is unknown, prove that $S^2$ is a sufficient statistics for $\sigma^2$. Likelihood: $$ L = (2\pi\sigma^2)^{-n/2} \cdot ...
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Comparing the overall mean of Monte Carlo simulation runs involving multiple observations

I have a set of n spatial points distributed across the landscape. I have hypothesised that the location of these points is determined by a property of the ...
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How to express descriptive statistics as statistical functionals - and why?

I'm reading through class notes explaining statistical functionals and came across the following expressions with little explanation how they were derived: Mean $=T(F)=\int xdF(x)$ Variance $=T(F)=\...
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How to derive second moment of the sample mean

Suppose you have $X_i$ be i.i.d, such that $E(X_i) = \mu$ and $Var(X_i) = \sigma^2$. I know $\overline{X}_n = \sum\limits_{i=1}^n X_i$ and, as is standard $E(\overline{X_n}) = \mu$ and $Var(\overline{...
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How does mean of data change in log transformation? [closed]

How does variance and mean of Y = log(X+1) change given we know the mean and variance of X which is also a lognormal distribution (Poisson Distribution). I figured that variance is smaller for Y ...
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Combining Estimates with Actual Values

I am exploring stature (living height), calculated from arm and leg bones, from an archaeological sample. Unfortunately, there are very few complete bones that can be measured and entered into the ...
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Credible Interval on 2 Random Variables

Assuming we have two random variables, $A$ and $B$, each are assumed to follow a normal distribution with unknown mean and variance. A random sample has been drawn from each $A$ and $B$. How is the 99%...
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19 views

One random sample Mean or 30 Random samples Mean

I have 30m records and i want to do a random stratified sample to estimate the mean based on predefined strata. Should i estimate the mean while taking 1 random (n=500) sample or to sample lets say 30 ...
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Approximating mean/covariance of truncated/folded/censored normal distribution

Given a normally distributed $X$, what is the best way to approximate the covariance matrix and mean vector of $\tilde{X} = \max(0, X)$? I am interested in the censored distribution, but the truncated ...
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Question about upgrading mean

Question: "Mabel is reviewing how much she paid her employees on average over the last work week. She had in her notes that her 9 employees were paid an average of \$450 each. After reviewing the ...
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What is the mean average of $y=kg^t$ from $t=a$ to $t=b$ [closed]

Mean average of $y$ in $y=kg^t$ from $t=a$ to $t=b$. $g$ is a constant, $t$ varies. I have looked this up in textbooks and online and all I can find is the mean average of a function where $t$ is a ...
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25 views

Normalize sample to match the mean and the standard deviation

There are two samples (sufficiently large and independent). One, size $n_1$ has the mean $m_1$ and the standard deviation $s_1$, the other, size $n_2$ with the mean $m_2$ and the standard deviation $...
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How to get the “reliability percentage” of a measurement

I need to get the amount of confidence I can have on a measurement (from 0 to 100 percent). In other words, I need to know how much reliable the data on a measurement is for me to trust its ...
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How to calculate the range from mean and SD?

Is is possible to calculate or estimate the range of a population if I know the mean, population size and standard deviation? I am doing a research and the mean age of the population is 29.9 +/- 5.3 ...
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ANOVA with small sample (duplicate)

I have a study with only a duplicate sample. I would like to know if there are differences between the 5 averages, each group has two samples. In another case, I have 3 averages and each group has 3 ...
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Uncertainty of a Mean from measurements with different uncertainties and of different items

I've searched around, but I am just not sure that the explanations I've found quite match up with what I am trying to do. Let's say I have 3 vials of a gas. For each vial, I measure some $T$, $P$, and ...
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Comparing yearly data that has different $n$ values per year?

I have been collecting soil moisture data at my research site for almost 20 years. However, I have not been consistent with the number of times that I have been taken these measurements. The problem ...
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How would a moment generating function change if all the random variables are increased by a value

Suppose you have some moment generating function $M_x(t)$ Now all the random variables x are increased by a arbitrary value b. What is the new moment generating value? I tried solving this by moving ...
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What is the mean absolute difference between values in a normal distribution?

I understand that variance is mean of squared differences and that standard deviation is square root of the mean. What, however, is the average difference between values in a normal distribution (...
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How is it possible for the arithmetic mean of a distribution to be off-center?

This is a question I recently saw on a test: "Consider the following statement: More than 65% of the residents of Los Angeles earn less than the average wage for that city. Could this statement ...
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How can I estimate the distribution of sizes if I sample from the tails of that distribution?

Let’s say I have an insect farm and they lay down a lot of eggs, which I collect in a cup. Now I want to study the size distribution of those eggs, but there’s a problem: The younger eggs, which are ...
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Is there a situation where you cannot do the T-test for mean inference?

So for mean inference, would there be a situation where you cannot use the T-test? Seems like you can always calculate a t-statistic, so it seems like you can always do the t-test for mean inference. ...
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Proportion of the sums or average proportion of the parts?

Here’s a curiosity that come up during a work discussion. While this example uses financial data, it has a statistical question at its heart. Consider the following table with a budget and actual ...
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Acceptable average difference value for scientific literature?

I have two instruments that measure the same parameter, I'll call them 1 and 2. 1 is calibrated and zeroed during the study and 2 is not calibrated and zeroed so the baseline values are all over the ...
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Should an observation always belong to the population to calculate its z-score?

It was mentioned in this link that, the standard score is the number of standard deviations by which the value of a raw score (i.e., an observed value or data point) is above or below the mean value ...
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Need help identifying a measure of central tendency, and how much a certain value deviates from it

So, I had asked a previous question for a problem that I am having. But, I don't think I framed it correctly, so I am trying to frame it more clearly here. Essentially, I have a skew normal ...
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Is it necessary for averaging amount of samples per class?

Say I have a mix of data from multiple sources, some classes have data up to around 200 whilst some have around 10~20 samples. (with negative samples ignored) Should I build my training, testing and ...
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Are this simple claim and its proof correct?

Suppose random sequence $\{X_{i}(N)\}_{i=1}^{N}$ is a row-wise i.i.d. triangular array, where $N$ is sample size. This means for any given $N$, $X_{i}(N),\dots,X_{N}(N)$ are i.i.d. following ...
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Paired T-test or Linear Mixed Model or what else?

I have measured 8 different features on the same mice on three different days. I want to compare the means of those 3 days based on the features. I have executed paired T-tests for each feature in the ...
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Mean then mult or mult and then mean

I have a dataset like the following structure: ...
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What situations using median is not recommeneded?

I was recently asked this question in an interview about when/where not to use median. I know median has some limitations such as it requires ordered list of numbers. But I am not sure if there is any ...
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Why taking an average makes convergence to zero faster?

Let $f(x,y)$ be some density, and let the leave-one-out Nadaraya-Watson estimator $\widehat{f}_{-i}(x,y)$ be defined as follows: $\widehat{f}_{-i}(x,y)=\frac{1}{(n-1)h^2}\sum_{j=1,j\neq i}^nK(\frac{(...
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Basic mean question

Learned today in stats this cool piece of information: If you wanted to optimize the $(y-\overline{y})^2$ or differences squared, of some data. Where $\overline{y}$ is a constant y = number, then you ...
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How can I develop a 0-100 composite or index score using multiple Z scores from multiple independent variables?

I'm really interested in index scores like the human development index or economic freedom index where they rank things on a 0-100 scale based off of a bunch of different variables (e.g. press freedom,...
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Is it valid to conduct a two sample t-test in this situation?

I know this is a real easy question, but I'm a little unsecure based on all that I read. I have a dataset with housing prices across a city. One of the variables also stores the postal-code. Now what ...
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Calculating the variance in throws made by a juggling machine

I have built a juggling machine. It has no sensors and moves in a consistent programed motion. In my attempts to make the machine juggle for as long as possible, I have been studying the accuracy of ...
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Difference between Sample Mean($\bar{X}$) and Expected Value (E[X])

I know this has been asked and answered, but many even have contradictory definitions as to which represents the mean of a probability distribution. I would like to cite: https://stats.stackexchange....
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Why use Welch's T-Interval or Pooled T-Interval For Mean Differences?

Let's say you have two samples from two populations, X and Y. You want to build a confidence interval around the difference in means of the two populations. Why not just always calculate a new ...
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Is regression towards the mean happening when we use a control group?

I have a subset of 40000 participants in my study. From those I would like to study those with higher weight longitudinally, and compare them with those with healthy weight. I observe, that those with ...

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