# Questions tagged [mean]

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

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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: $\mu = \frac{1}{N}\sum_{i=1}^N{x_i}$ (1) $\frac{1}{N}\sum_{i=1}^N{(x_i-\mu)^2}$ (2) Then do we assume, that the data are ...
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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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### 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 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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### 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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### 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 ...