# Tagged Questions

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

7k views

### Difference between standard error and standard deviation

I'm a beginner in statistics. I'm struggling to understand the difference between the standard error and the standard deviation. How are they different and why do you need to measure standard error? ...
7k views

### Which “mean” to use and when?

So we have arithmetic mean (AM), geometric mean (GM) and harmonic mean (HM). Their mathematical formulation is also well known along with their associated stereotypical examples (e.g., Harmonic mean ...
3k views

### Averaging correlation values

Let's say I test how variable Y depends on variable X under different experimental conditions and obtain the following graph: ...
2k views

### Maximum value of coefficient of variation for bounded data set

In the discussion following a recent question about whether the standard deviation can exceed the mean, one question was raised briefly but never fully answered. So I am asking it here. Consider a ...
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### How should one interpret the comparison of means from different sample sizes?

Take the case of book ratings on a website. Book A is rated by 10,000 people with an average rating of 4.25 and the variance $\sigma = 0.5$. Similarly Book B is rated by 100 people and has a rating of ...
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### Is Amazon's “average rating” misleading?

If I understand correctly, book ratings on a 1-5 scale are Likert scores. That is, a 3 for me may not necessarily be a 3 for someone else. It's an ordinal scale IMO. One shouldn't really average ...
450 views

### Example of distribution where large sample size is necessary for central limit theorem

Some books state a sample size of size 30 or higher is necessary for the central limit theorem to give a good approximation for $\bar{X}$. I know this isn't enough for all distributions. I wish ...
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### How to compute the confidence interval of the ratio of two normal means

I want to derive the limits for the $100(1-\alpha)\%$ confidence interval for the ratio of two means. Suppose, $X_1 \sim N(\theta_1, \sigma^2)$ and $X_2 \sim N(\theta_2, \sigma^2)$ being independent, ...
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### Significance tests

I have two sample means from two different samples. I purport that the true population means are identical. $H_{0}$: $\mu_{1}=\mu_{2}$ and $H_{1}$: $\mu_{1}\ne\mu_{2}$ What significance test would I ...
19k views

### Why is median age a better statistic than mean age?

If you look at Wolfram Alpha Or this Wikipedia page List of countries by median age Clearly median seems to be the statistic of choice when it comes to ages. I am not able to explain to ...
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### Can the standard deviation of non-negative data exceed the mean?

I have some triangulated 3D meshes. The statistics for the triangle areas are: Min 0.000 Max 2341.141 Mean 56.317 Std dev 98.720 So, does it mean anything particularly useful about the standard ...
820 views

### Is it appropriate to plot the mean in a histogram?

Is it "okay" to add a vertical line to a histogram to visualize the mean value? It seems okay to me, but I've never seen this in textbooks and the likes, so I'm wondering if there's some sort of ...
691 views

### Does a univariate random variable's mean always equal the integral of its quantile function?

I just noticed that integrating a univariate random variable's quantile function (inverse cdf) from p=0 to p=1 produces the variable's mean. I haven't heard of this relationship before now, so I'm ...
136 views

### Question about squares of the coefficients of variation

Suppose that $X$ is a random variable with any distribution that takes only positive values. Can the following inequality hold for constants $c_2 >c_1 >0$? ...
3k views

### How do I calculate a confidence interval for the mean of a log-normal data set?

I've heard/seen in several places that you can transform the data set into something that is normal-distributed by taking the logarithm of each sample, calculate the confidence interval for the ...
305 views

### How can I test $H_0:\sigma^2_1=\sigma^2_2$?

I have a few hundred estimates of a parameter calculated from two different models and I would like to know if these parameters have different variances. What is a straightforward test for comparing ...
530 views

### Why are cumulative residuals from regression on stock and index returns mean reverting

In the paper M. Avellaneda and J. H. Lee, Statistical arbitrage in the U.S. equities market, July 2008, in the Appendix on page 44, I have some questions. First he runs the regression of ...
262 views

### Comparing 2 independent non-central t statistics

One estimate of the 'quality' of a portfolio of stocks is the Sharpe ratio, which is defined as the mean of the returns divided by the standard deviation of the returns (modulo adjustments for risk ...
345 views

### Mean$\pm$SD or Median$\pm$MAD to summarise a highly skewed variable?

I'm working on highly skewed data, so I'm using the median instead of the mean to summarise the central tendency. I'd like to have a measure of dispersion While I often see people reporting mean ...
347 views

### Calculating the mean using regression data

I have some data to analyze where $y$ is dependent of $x$ - a linear regression was used. It's a question from an exam, so I think it should be solvable. The regression was used to estimate the mean ...
10k views

### How to calculate the truncated or trimmed mean?

How can I calculate the truncated or trimmed mean? Let's say truncated by 10%? I can imagine how to do it if you have 10 entries or so, but how can I do it for a lot of entries?
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### Question on confidence interval

My mean is 3.454992884900722e+008, and my confidence intervals from three distributions (when compared to the given mean) are: CI for dist. 1: 1.0e+008 * ...
62 views

### How to define the multiplier range for variance test based outliers detection algorithm?

I have a variance test based outliers detection algorithm. The algorithm is exposed with a visual application where the user can configure its parameters namely the multiplier. The question is what ...
620 views

### Transform Data to Desired Mean and Standard Deviation

I am looking for a method to transform my dataset from its current mean and standard deviation to a target mean and a target standard deviation. Basically, I want to shrink/expand the dispersion and ...
471 views

### Difference in means in multiple-choice poll

Let's say that N randomly chosen persons where asked a question where the answer could be in either of X categories. For example, 500 persons where asked which of the top 5 political parties they ...
255 views

### One component in PCA is always the mean vector in two-dimensions but not three

I've been testing PCA via SVD to decompose a simple time series data matrix, $X$. I have two signals $x_1(t)$ and $x_2(t)$ in a data matrix where $M$ rows represents each timepoint sample and each ...
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### Two sample t-test for data (maybe time series) with autocorrelation?

I am new to statistics, so pardon any mistakes in my question. I have two time series $X_i$ and $Y_i$. Assuming that they're stationary AR(1) processes with possibly different means, how do I test ...
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### Mean and covariance of a mixture of two distributions

This is a homework problem. If I could have some hints on how to solve it that would be great. Mean and Covariance of a Mixture of Two Distributions:  I = \left\{ \begin{array}{l l} 1 ...
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### Finding a linear relationship without linear model

(If this doesn't make sense it is because I am inexperienced at statistics) Assume I have a broad universe of actions $A$ I could pursue, and for each $a_i \in A$ there is an associated ...
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### Calculating mean age from grouped census data

I hope you can help me with a question regarding calculating mean age from grouped census data. If the age categories used were [0–4], [5–9], [10–14], and [15–19] years, how would you calculate the ...
1k views

### Why (or when) to use the log-mean?

I am looking at a scientific paper in which a single measurement is calculated using a logarithmic mean 'triplicate spots were combined to produce one signal by taking the logarithmic mean of ...
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### Is it typical for group means of composite z-scores to have means with values of the same magnitude but opposite signs?

I developed a composite score by converting four items to z-scores, then I summed up the z-scores to form a composite measure. However, when I've calculated means to compare finding for two ...
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### Reason for taking the mean of experimental observations

Whenever we do some experiment in Physics, e.g. measure Planck's constant, we take the mean of several experimental observations. This seems to be the most obvious way to report a result. Is there a ...
Suppose that I want to study the relationship between two variables $Y$ and $X$ using the linear model $Y \sim X$. Unfortunately, both $Y$ and $X$ are not normally distributed, say they are both ...