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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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216 views

Generalizing the mode and mean like the quantile

The mode, median, and means of a series of number ($x_1,x_2,...,x_N$) can be roughly thought of as the points that minimize the $p$-norm of the sequence for $p\in \{0,1,2\}$. The median is $c=\min_c\...
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Pearson Correlation Coefficient for samples $X,Y$ equals $1$ iff there is $a>0, b\in \mathbb{R}$ with $x_i = ay_i + b$ for every $i=1,\dots,n$.

Let $X = (x_1,\dots,x_n)$ and $Y = (y_1,\dots,y_n)$ be outcome values. We have defined the variances $s^2_X = \frac{1}{n-1} \sum_{i=1}^n (x_i - \bar{x})^2$, $s^2_Y = \frac{1}{n-1} \sum_{i=1}^n (y_i - \...
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69 views

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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18 views

How to calculate weighted average of hourly sales in a day

I have hourly sales data & want to aggregate it to a day level. Out of $24$ hours, we are classifying $6$ hrs as peak hours and $18$ hrs as non-peak. Assume peak hr sales for a day as: $X_1, X_2,...
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24 views

What questions lead to different representative statistics?

What are the questions that are asked whose answer yields the geometric and harmonic means. For example, we arrive at the arithmetic mean by solving: $$ \min_y \sum_{x \in S} (x - y)^2$$ What ...
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68 views

What is the meaning of subsampling level in machine learning/statistics?

I am reading a paper but nowhere it is defined but the term is being used a lot. The paper is - Less is More : Nystrom Computational Regularization -Rudi,Camariano, Rosasco Link : ...
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320 views

Calculating median (second quartile) using formula for quartiles in an interval

I have the following formula in my lecture notes for calculating the $j^{th}$ quartile in an interval: $$Q_j=L_l+I\frac{N \frac{j}{4}-F_l}{f_l}, j=1,2,3$$ Where $L_l$ is the left side of the ...
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89 views

statistical tolerance limits

My Question is: What statistical methods can be used to examine whether a selection of tolerance limits of data makes sense, i.e. validation of tolerance limits? My solution: I would analyse how many ...
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36 views

1-How my profesor reach this solution? 2-How can I use eigenvalues to compute betas?… if there is any way

this time I quite don't undertand how the profesor avoid using matrix algebra to solve this exercise. Statement: Below you can see a scatter plot of the data with the three regression lines ...
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1k views

Joint PDF of Chi-Square & Normal Distribution

Let the independent random variables X1 and X2 be N(0,1) and $\chi^2(r)$, respectively. Let $Y_1$ = $X_1/sqrt(X_2/r)$ and $Y_2$ = $X_2$ a) Find the joint pdf of $Y_1$ and $Y_2$. b) Determine the ...
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317 views

Concrete examples concerning standard deviations and mean absolute deviations

Is there a simple (or not simple?) algorithm that will churn out examples of pairs of moderately small finite multisets (hereinafter calls "sets") of moderately small integers satisfying the following ...
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16 views

What kind of statistical test should I use to compare a variable between two groups? (Problem i found at work)

I work for a bank in south america and we do something called elasticity price test to determine what is the best "Price" (fee for a product), here is how it goes: We select two similar groups and ...
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31 views

Expectation for a $\chi^2_n$ distributed random variable.

Consider $X_1,\ldots, X_n\sim\mathcal{N}(\mu,\sigma^2)$ iid, where $\mu$, $\sigma^2$ are unknown and $c>0$. Define $$S_n^2:=\sum_{k=1}^n\Big(X_k-\frac{1}{n}\sum_{i=1}^nX_i\Big)^2$$ Now I want ...
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19 views

Sum and sample of binomial distributions

I have an assignment with the popular defective machines etc, where we're called to create a function that will calculate the amount of defective articles in a sample n from the Total N. Keep in mind ...
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15 views

Evaluating the effect of starting position on the finishing position of a race

I have a set of data giving the finishing place of 10 people in a number of races. Each race starts with the racers in single file with a set distance between each racer. I want to evaluate how the ...
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30 views

Interpolation Polynomials with Integer coefficients

Suppose we have an ordered list of real values: $$x_1,x_2,x_3,...,x_N \in \mathbb R$$ Now if we consider the set in $\mathbb R^{2}$ (ie with their ordering index as the first variable) : $${\{(1,...
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410 views

How to interpret the results of Kolmogorov-Smirnov test in SAS?

I'm obtaining this results ins SAS and I'm pretty sure that the sample is normal, but I'm unable to interpret the KS test, so I put this images and the results that I obtained from SAS in order to get ...
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33 views

Calculating Variance $V\big\{-\frac{2}{\sum_1^n x_i}\big\}, \; X_i \sim \Gamma(2,1/\theta)$

I have some trouble calculating the following variance : $$V\bigg\{-\frac{2}{\sum_1^n x_i}\bigg\}$$ where $X_i$ follow the Gamma Distribution $\sim \Gamma(2,1/\theta)$. Attempt : $X_i$ are ...
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105 views

How can one quantify the convergence of relative frequency to probability?

I have a rather basic question about statistics but I am unable to find an answer in the literature I have at hand. Say I run a simple Bernoulli trial a number of times and compute the relative ...
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31 views

Averaging non-independent variables

I am looking at the data on the Estimated U.S. Waste of Food percentage on the table here. I want to determine how "impactful" the variables "Children under $18$ in household" and "Household income ...
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318 views

normal distribution, mean = 80 and standard deviation = 5. score? separates the top 10% of the scores from the lowest 90% of the scores

Checking my work: M = 80 SD = 5 X = ? scored 90% better than others. Closest area from table was .8997 giving a z-score of 1.28. using the formula z = (x - M)/SD, my answer is 86.4
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19 views

statistics of detector efficiency

Can anybody help me with this question? If a trigger requires hits in some minimum number of layers when the whole setup com prises 12 detectors layers, what is the fraction of events that are ...
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320 views

Statistic Class Boundary

I have a set of data in exclusive form. The Time(class limit) is from 0-20, 20-40, 40-60, 60-80 and 80-100. The frequency in bracket of each classes are as follow 0-20(f=2), 20-40(f=15), 40-60(f=20), ...
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40 views

Characterization of the binomial estimator

In my study of the minimum variance unbiased estimators, I found two facts that I can not underestand: If $X$ has a binomial distribuition with parameters $ n = 1$ and $\sqrt\theta$ (Berboulli case),...
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37 views

Median income and unemployment rate in a region with no residents

It was a satire article that sparked this question, in which the median income was stated to be \$$0$ and the unemployment rate to be $100\%$ in a particular area (the Mariana Trench in the western ...
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0answers
25 views

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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0answers
58 views

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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57 views

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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17 views

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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301 views

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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14 views

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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37 views

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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38 views

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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358 views

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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166 views

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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55 views

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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66 views

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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80 views

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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56 views

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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34 views

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 ...
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106 views

Concrete example : likelihood, comparing theory and practice (genetic linkage)

Crossing tomato plants should give birth to a new population of plants of 4 types that we'll call $P_1$, $P_2$, $P_3$ and $P_4$. According to theory, the ratios of appearance of these 4 should be $\...
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29 views

Curve 'anti-correlation' detection

If I have a data set, what algorithm can I use to detect when one curve moves in clear opposition to the majority of curves? For example: At point 15, the purple line moves up in opposition to the ...
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0answers
1k views

Calculating the median when the sample size is even

In statistics the median is a point that divides an ordered data into two equal parts. By definition if $n$ is odd the median is $\frac{n}{2}{th}$ data point that is simply the middle point of the ...
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435 views

Harmonic F statistic

i am interested what does mean Harmonic F statistic in mathematical language?i have search about $F$ statistic and found a lot of explanation,for example like this "**F Statistic The F statistic ...
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72 views

Identifying modes in circular data

I have some circular data (ie, angles in $[0, 2\pi)$), and I need to analyze it in terms of its modes. I hope this is the right place to ask for help solving this. The main thing I need to be able to ...
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0answers
81 views

How should I measure the “fit” between two sequences?

This question is for a machine learning application, which, surprisingly, is not stock price prediction. I apologize for being overbroad, but any ideas or even help framing the question would be ...
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0answers
607 views

quantile rank formula

I am teaching a basic statistics course for psychology students. The lecturer provided a formula for the rank of a quantile rank = alpha n + 1/2, alpha being the proportion which corresponds to the ...
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6 views

link function interpretation for models

In the categorial regression using the logit link function, the estimated coefficients are used to calculate the odds ratios or the ratio between two odds, that is, the model is interpreted through ...
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0answers
19 views

EWMA and EWMV unbiased estimators

Good evening. I got random variables $r_1, r_2 ... r_N$ i.i.d normal with mean $\mu$ and variance $\sigma^2$ I also got $\lambda$ - decay factor. I got 2 estimators: $r_N^{*} = \frac{1 - \lambda}{...
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0answers
16 views

How to infer the underlying distribution of a statistic (Bayesian inference?)

I have a list of approximately 30,000 venues in a major US city. These venues hold all kinds of events, sports, conferences, concerts etc. I want to know the distribution of the 'capacity' of these ...