# Questions tagged [descriptive-statistics]

The area of statistics that provides descriptions of data, may it be samples or the population. This includes graphical representations and numerical indicators. No information is inferred from samples about the population, as in inferential statistics.

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### How do I state that a data set has a 'denser' standard deviation?

Suppose I have two algorithms that produce numerical data. The first algorithm produces { 2452, 695, 318, ... } with a mean of 1155 and a standard deviation of 1138. The second algorithm produces { ...
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### extracting meaning out of graphs

i was given graph and five statements and i was told to choose the correct statements based on the graph in the graph is showing the weight of boys over time in the red line and of girls in the ...
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### Deriving 68% confidence level for each parameter after MCMC

I used the MCMC package https://github.com/joshburkart/mathematica-mcmc to find the best parameters for model of Massive Gravity. Now I need to find the confidence 68% for each of those parameters and ...
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### Estimate the median from mean, variance etc.

I'm given four groups containing 15 observations each. I can only see a few of the observations. However, for each group, I'm given the variance, mean, sum, USS, SSD etc. I have to estimate the ...
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### Relationship between Var(X) and Var(Y) where y(i) = ax(i) + b

This is a question that appears in our textbook. "Let a and b be constants and let y(i) = ax(i) + b for i = 1, 2, ..., n. What is the relationship between Var(X) and Var(Y)?" We have then that Var(Y)...
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### CUSUM Algorithm

One commonly used changepoint detection test is the CUSUM algorithm. It performs optimally when the pre-change mean and variance of the process are known, $μ_1$ and $\sigma_1$ is required. Then the ...
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### What is the appropriate metric for these two values?

For a test suite I have, each test has a failure rate (from 0 to 1), where 1 means it fails every time and 0 means it never fails, and a duration in ms (this is unbounded). I want a metric (I think ...
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### Probability Poisson sample mean convergency

Let $X_1,\ldots,X_n$ be a random sample of Pois$(1)$. Then: $$P\left(F\left(\bar X_n\right)<F(1)\right) = P\left(\bar X_n<1\right) \to 1/2$$ as $n \to \infty$. Is this true and if so, why or ...
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### Standard Error: multiplied or divided by SD?

I'm relearning stats after a number of years of non-use, and I have a great textbook I'm using which defines the SE as the square root of the number of draws from a box multiplied by the standard ...
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### Find p-value? Multiple regression analysis

I want to know can I find the approximate p-value for (beta)𝛽2 if you were to test a hypothesis? How do I do that? \begin{align} n & = 30 \\ \hat y & = 123.2 + 4.59x_1 + 1.25x_2 − 6.04x_3 \\ ...
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### Moving Window Computation of Skewness and Kurtosis

I would like to be able to calculate Skewness and Kurtosis from a sliding window dataset in a computationally efficient manner. The dataset shall be a specified quantity with new elements replacing ...
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### Directional Statistics: Computation and Interpretation of Histograms of Directional Data

Suppose $v$ is a unit random vector in $R^n$ and consider a set $V = \{v^1,v^2,\dots\}$ of samples of $v$ gained either through experiments or simulations. How do we compute and interpret the ...
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### maximum entropy principle: CDF of its PDF

In goodness-of-fit (gof) tests (COD, R2, X2) to discriminate PDFs, we need their CDFs. With wind speed, another PDF is by Maximum Entropy Principle or Method, of the form: f(v)=\exp\left\{-a_0 - ...
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### Best way to compress a noisy observation

Say we have a discrete signal $X\in \mathcal{X}$, and a noisy observation $Y\in\mathcal{Y}$. We wish to encode $Y$ into some encoding $U$ with rate $R$. That is, $H(U)=R>0$. And we want $U$ to have ...
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### Is the following data set possible?

"Is it possible to create a data set where $\bar{x}=30.0$, range $R=10$, and variance $s^2=40.0$?" I feel sort of dumb asking this question, but I'm not quite sure I'm on the right track. I know that ...
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### Normality assumption of MANOVA

Data set has 2 dependent variables and 1 independent variable with 3 groups. Normality assumption of MANOVA says that variables has to be normally distributed within the groups. My data set has 30 ...