Questions tagged [mean]
The expected value of a random variable; or a location measure for a sample.
2,221
questions
0
votes
0answers
10 views
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: $\mathrm{E}(u|x)=\mathrm{E}(u)$
...
0
votes
0answers
32 views
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 = \...
0
votes
0answers
14 views
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!!
19
votes
6answers
2k views
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 ...
1
vote
2answers
25 views
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 ...
5
votes
1answer
93 views
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 ...
1
vote
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=...
0
votes
0answers
5 views
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) ...
1
vote
1answer
16 views
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 ...
1
vote
1answer
17 views
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 ...
0
votes
0answers
8 views
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 ...
0
votes
0answers
56 views
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 ...
0
votes
0answers
29 views
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 ...
5
votes
2answers
331 views
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)=\...
0
votes
1answer
47 views
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{...
0
votes
0answers
10 views
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 ...
2
votes
1answer
27 views
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 ...
0
votes
0answers
21 views
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%...
0
votes
1answer
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 ...
0
votes
0answers
18 views
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 ...
0
votes
0answers
10 views
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 ...
1
vote
1answer
16 views
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 ...
1
vote
1answer
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 $...
1
vote
0answers
35 views
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 ...
4
votes
2answers
129 views
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 ...
0
votes
0answers
14 views
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 ...
1
vote
0answers
17 views
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 ...
2
votes
2answers
31 views
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 ...
0
votes
1answer
18 views
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 ...
8
votes
1answer
404 views
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 (...
1
vote
1answer
26 views
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 ...
2
votes
0answers
22 views
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 ...
1
vote
1answer
34 views
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.
...
1
vote
1answer
24 views
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 ...
0
votes
0answers
12 views
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 ...
1
vote
1answer
35 views
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 ...
0
votes
0answers
28 views
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 ...
0
votes
0answers
8 views
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 ...
1
vote
0answers
37 views
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 ...
0
votes
1answer
15 views
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 ...
0
votes
1answer
17 views
2
votes
1answer
36 views
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 ...
1
vote
1answer
105 views
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{(...
0
votes
2answers
43 views
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 ...
1
vote
1answer
23 views
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,...
1
vote
2answers
40 views
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 ...
3
votes
1answer
19 views
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 ...
0
votes
0answers
23 views
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....
0
votes
1answer
17 views
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 ...
0
votes
0answers
14 views
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 ...
