Questions tagged [mean]

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

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10 views

How to calculate the confidence interval of a mean on web search findability

I have 30x 1-hour sessions where I assign one random person to each session to search for a specific type of content on a social media website. I record the number of pieces found in each session, ...
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Calculating the mean clearance time between stages

I'd like to compute the mean stage clearance time btween stage 1 and stage 2. The mean stage clearance time for stage 1 is calculated as follows: Stage 1: 100 people(100 people participated) Stage 2: ...
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How to compute (and use) a confidence interval for binary classification probabilities

I have a trained image classifier and 30 test images, 24 of which are classified correctly. With a decision boundary of 0.5, the remaining 6 images are misclassified as false positives. I'd like to ...
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24 views

How to calculate mean and proportion from a binomial distribution?

Lets say that I flip a coin and get heads 50/200 times. What would my proportion and mean be for this binomial distribution? I am getting confused, because in a binomial distribution there are only 2 ...
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33 views

How do we calculate the variance of normal distribution where the mean also has normal distribution?

Now I have $y_i \sim N(\mu_i, \sigma^2)$, where $\mu_i \sim N(\mu, \tau^2)$. Could anyone explain how to calculate the variance of $y_i$? Does $y_i$ also has variance $\sigma^2$? Or has variance like $...
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Test multiple differences of means (multivariate t test)

Let's say I have a dataset with two groups (male and female), a target variable ($y$) and multiple features ($X_1$, $X_2$ and $X_3$). gender y X1 X2 X3 m 100 39 150 12 m 120 44 180 16 f 100 22 140 ...
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1answer
27 views

Can we predict what happens to the sample mean as we increase sample size if the true mean blows up?

The Cauchy distribution is used as an example of a pathological case where the mean blows up. For such a distribution, we can imagine drawing samples and tracking the sample mean as the number of ...
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Why are hypothesis tests still used when we have the bootstrap and central limit theorem?

Why are hypothesis tests still used when we have the bootstrap and central limit theorem? To give context to my question, I briefly go over the central limit theorem and illustrate a simulation ...
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How to solve this problem? [closed]

Given the two sample distributions in classes: Calculate arithmetic means and distinct (biased) sample variances and overall. Determine if there is stochastic dominance or not. I have the solution ...
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1answer
54 views

Does averaging affect statistics?

I have an array that represents client's bills for a certain period of time. Each client has several values. I need to group data by week or month and calculate mean and variance. However, I have a ...
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Difference in using mean of log(X1),log(X2)...log(Xn) vs. geometric mean (X1,X2,Xn)?

I have positively skewed data that I had to transform to log(). The observations are distributed across 3 groups. For example, in group #1: I calculated the geometric mean of the raw data (GM = 224), ...
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Limitations of cumsum_shift function for reverse moving average [closed]

I'm using your cumsum_shift function in my large df (400,000 points) but I have problems when I change the win_size. Figure below is for win_size=12,000 and I can see some spikes at the end of each ...
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44 views

Frequentist Justification for using Student's t-Distribution to Construct Confidence Intervals

In my most recent statistics class, the general1 frequentist approach to constructing confidence intervals2 for an estimator (of any kind) was described as follows: Specify the estimator and the data ...
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Applications of "Regression Towards the Mean" in Real Life

I was reading about "Regression Towards the Mean": (https://en.wikipedia.org/wiki/Regression_toward_the_mean). Over here, an explanation of this concept is provided: "Consider a simple ...
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1answer
365 views

How can I better understand this covariance equation?

This is the equation given to me in the lectures: $$S=\frac1N\sum_{n=1}^N(\mathbf{x}_n-\overline{\mathbf{x}}) (\mathbf{x}_n-\overline{\mathbf{x}})^T,$$ which doesn't make sense to me when I think ...
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Estimating the Population Mean with the Sample Mean

I am trying to better understand how the sample mean can be used to estimate the population mean. Using the R language, suppose I have the following population: ...
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Comparing two distributions of R² values of regression models built using bootsrapped subsets of data?

Added more details to an earlier (now deleted) post. About whuber's earlier suggestions to look at questions about variable selection: I tried looking on the forum regarding similar issues but I am ...
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1answer
30 views

Usage of t-test group level vs. individual level combined

I have a study about sprint running. Study consists of 16 participants, each performed 7 sprints. This results in a CMC value in evaluating the validity of a new measurement system with 7 per ...
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How Well Does the Mean Describe a Multimodal Probability Distribution?

When you have highly skewed, irregular or multimodal distributions: In these instances, does it become more advantageous to use the median instead of the mean to infer properties of these ...
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8 views

Aggregate Differences From Multiple Groups

My goal is to estimate the average difference in running speed over 1 km between men and women percentage increase in running speed over 1 km of men over women The participants are in 23 different ...
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1answer
64 views

Simple comparison of two Poisson means in R?

I have two samples and I would like to determine whether the difference between them is statistically significant or not: Because this is clearly data of small counts that cannot be approximated by a ...
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1answer
49 views

Can I use unpaired t-test to test the difference between the means of two categories extracted from different questionnaires?

I have 40 questionnaires, each one consists of one question comparing two variables A and B. A and B in these 40 questionnaires are different forms of two categories X and Y. ...
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1answer
22 views

Weighted mean based on standard deviation

I have a set of estimates, each with a confidence interval that has its own standard deviation. I want to find the mean of the estimates (red dots in figure), but weight them based on the confidence ...
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1answer
60 views

Median of Means notes proof wrong?

My main question is about the last step in the proof of one property in this short notes about the method of Median of Means(MoM) estimator. The Proposition is stated as follows: Proposition 1 Assume ...
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1answer
41 views

Standard deviation always larger than the mean -- implications [closed]

I was working on a series of calculations, and in my work, I came to the conclusion that (with some help from Jensen's inequality) that the following property holds: $$\sqrt{\text{Var}(X)} > \...
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28 views

Mean of values with individual random errors

I have 3 values and each of them have some random error to them. These values have no correlation with each other and neither do the errors. I want to find the mean of these values and the standard ...
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Differencing in coefficient of variation

For a project, I am trying to estimate the variability of an atmospheric variable across N years using the coefficient of variation. Let's call this the estimated ...
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Which method to use to compare a mean to the means from past surveys?

I have data for every year. The big dots are the means for every year. The lines are only to visualize the difference between means. Every mean in every year is based on an individual sample/cohort. ...
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1answer
29 views

Difference between RMSE Mean vs RMSE Std?

I had two datasets that I wanted to cross validate using xgb.cv. I used a pandas dataframe, split each it into 2 where X = what I wanted to predict, y = features. ...
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Using the coefficient of variation to detect feature importance - but what if mean and sd are correlated? [closed]

I would like to have an estimate for the importance of a feature - the rough idea would be to define importance as the ratio between the mean and standard deviation. In other words, a feature is ...
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Question regarding the IQR

I have a question regarding some homework for uni: The variable "number of points per game" has a mean of 25, a median of 30, and an interquartile range of 20. Which of the following ...
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What can we infer from the sample size and mean?

I came across this interesting question today and haven't been able to understand how the statistician was able to arrive at the estimate: A sample of 300 customers were asked to participate in a ...
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1answer
38 views

Mean and standard deviation comparisons

I have datasets (one 1997-2001, another 2020, 2021) with means and standard deviations that I need to compare. Two different dats information (mass and total number). It is expected that I compare ...
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Determining the precision of a range

Supposing that I have 2 measured values which cover a range Y and Z and the actual value "X" is somewhere in the middle. How can I calculate the precision of the range? I expected to ...
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23 views

What is the formula for the Mean & Variance for this Log Normally Distributed Variable

I am having trouble finding the mean and variance for this log normal distribution.
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Changes in overall mean as a consequence of group composition vs. group-wise mean shifts

The mean body size of an entire community might shift due to different mechanisms and as a consequence of e.g. "changes in the relative abundances of different age-classes [...] within the ...
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1answer
37 views

Understanding the Importance of "Sufficiency" within Statistics

I am trying to better understand what it means to be a "sufficient statistic". "In statistics, a statistic is sufficient with respect to a statistical model and its associated unknown ...
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1answer
31 views

How does Michaud Resampling improve Mean-Variance Optimization?

Michaud Resampling claims to reduce estimation error through the following process: Step 1. Sample a mean vector and covariance matrix of returns from distribution of both centered at the original (...
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187 views

Right way to compute mean and variance

If I take as definition of $a_{lm}$ following a normal distribution with mean equal to zero and $C_\ell=\langle a_{lm}^2 \rangle=\text{Var}(a_{lm})$, and taking the following random variable $Z$ ...
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1answer
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Convergence in distribution for difference in sample means?

Suppose $X_i, i=1,\ldots, n$ are $i.i.d.$ random variables with mean $\mu_X$ and variance $\sigma^2_X$ $Y_j, j=1,\ldots, m$ are $i.i.d.$ random variables with mean $\mu_Y$ and variance $\sigma^2_Y$ $\...
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1answer
34 views

How to estimate mean confidence intervals for a sample of a population with the population standard deviation?

First off, this is my first question on stats exchange. So if I mess up or anything, please let me know because I know this website is a lifesaver, and I want to spend more time on it. Recently, I ...
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Comparing 2 sample means

I'm trying to quantify the difference between two sample means. I'm not sure if I can use the standard two sample t-test. The first sample comes from the difference of two time series (inflation rate ...
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32 views

On average what is the norm of a sample from a multivariate normal distribution? [duplicate]

Problem Suppose I sample a multivariate standard normal sample $x \sim N(0, I_d)$ where $d \geq 1$ is the dimension. What is the expected value of the norm of $x$ $$ \mathbb{E}[\|x\|] = ? $$ Using ...
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1answer
36 views

How can I make an existing time series more volatile?

I have an existing time series that I would like to make more volatile, or more variance. I would like the highs to be higher and the lows to be lower. The time series is somewhat stationary and I ...
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1answer
15 views

Difference between Hmisc::describe() and base::mean()

I am currently using the function Hmisc::describe() to work on a dataset, but I am a bit confused by the fact that I get different mean results between the mean ...
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1answer
44 views

Why do 95% confidence intervals contain the unknown population mean 95% of the time?

I am learning about the Central Limit Theorem (CLT) and confidence intervals from this online course. I have learnt that that the CLT states that the theoretical sampling distribution of a sample ...
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How to calculate the distribution of the sample mean of uniform distribution? [duplicate]

I am working on the following question but I'm not sure if my approach is correct. Given that X~U(4,8), I need to find the distribution of the sample mean for a sample size 30. My approach is that ...
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1answer
72 views

testing whether a sample of the population has a different mean than the population mean

I have a short question regarding testing whether multiple subsample means are different from the population mean. To be specific, I have the full population of the energy consumption per square ...
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Geometric Brownian motion drift estimation problem

Given: $$ d \ln{S_t} = \left( \mu - \frac{\sigma^2}{2} \right)dt+ \sigma dW_t $$ We have that: $$ \mathbb{E}_t[d \ln(S)]=\left( \mu - \frac{\sigma^2}{2} \right)dt $$ $$ \mathbb{V}_t[d \ln(S)]=\sigma^2 ...
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Covariance of the means of $x_t$ and $y_t=(x_t-\bar{x})^2$

Given a sample of a real-valued time series, $x=\{x_t\}_{t=1,...,T}$, let $\bar{x}$ be the sample mean of $x$ and set $y_t=(x_t-\bar{x})^2$. Then, $\bar{y}$ estimates the variance of $x$. Question: ...

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