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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Using Chebyshev inequality

Supposing $X \sim \mathcal{N}(\mu=9,\sigma^2 = 4)$ use Chebyshev inequality to approximate the maximum value of $\mathbb{P}((X\le6) \cup (X>12))$ and compare with exact value.
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How to discern between results with and without defects using statistics?

I need advice on the statistical method, and I've included some preliminary findings from my dataset, which includes mean, standard deviation, and variance. To distinguish between artifact-related and ...
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Calculating the first and second moments for the sum of functions of random variables

I am trying to calculate the first and second moments of a sum of $M$ functions, where each function $f(x_{m})$ takes a random variable $x_{m}$ as an argument. I would like to compare the calculations ...
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Distribution of a double-sum

I have some random variables $X_1, X_2, X_3, ...$ that are normally distributed with mean 0 and standard deviation $\sigma$. I am trying to model a function of these variables that includes a double-...
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Power Analysis for multiple distributions

I have 3 groups I want to study using a single independent variable. In particular, I wish to know the sample size needed for each group. In the case of having 2 groups, it seems power analysis ...
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Percentile of a discrete distribution with degenerate scores

I have a ranked dataset of 100 entries, where 10 entries have score 1 and 90 have score 0. How to interpret the first percentile of this dataset? Does this consist of the 10 entries with score 1? If ...
TobiR's user avatar
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Is it possible for most (all?) items in a list to lie within one standard deviation of the mean of that list?

Question. Is it possible for most (all?) items of a list to lie within one standard deviation of the mean of that list? Motivation. Fast computations of approximate medians of lists of integers is ...
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Range of correlation between *Stacked* Variables

Similar questions have been asked before where we have Cor(X,Y) and Cor(X,Z) and we want to find out the range of correlations of sum linear combination X & Z with Y. Or a third correlation: (X,Z)....
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Strange equality involving the sum of squares of a finite set in Euclidean vector space

Conjecture. Let $Q$ be a finite subset of a finite-dimensional Euclidean vector space $V$ and let $p \in V$. Then $$\sum_{q \in Q} ||q - p||^2 = \sum_{q \in Q} \left(||q - \mathbb{E}[Q]||^2 + ||\...
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Fitting a line to the outermost plot on a graph

I am plotting the nonlinear regression on some fatigue data. My goal is to create a line that adheres to the slope line (in red). This line should sit beneath the lowest point on the left side of the ...
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Comparing statistical features extracted from time series using correct distance metrics

I would like to cluster 400 car rental demand time series (small positive valued) based on the following 7 statistical features: entropy, number of mean crossings, 95th percentile, root mean squared, ...
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Strange distribution of movie ratings

I like math but I also like movies. I have been collecting movies all my life. My collection is rather huge: almost 25.000 movies. Being also a developer I was able to create my own online catalogue ...
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How did the concept of quartile and Inter-quartile Range came into existence?

What is the sequence of historical events that led to the creation of the concept of quartile and Inter-quartile Range? And while calculating IQR, why do we consider the 75th percentile as the upper ...
Digvijay Singh's user avatar
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Is the following definition of Inter-quartile Range or IQR correct? If yes, then is there any published literature to support it?

It is the difference between the upper and lower quartiles; hence, it does not include extreme values present in the data. To calculate IQR, first, the data should be arranged in ascending order. Now ...
Digvijay Singh's user avatar
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Statistical indexes order in an asymmetrical distribution

I was wondering what's the order between mode, median, arithmetic mean, geometric mean and harmonic mean in a distribution with positive skewness and in another with negative skewness. Which are the ...
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Given descriptive stats for two sets $(x_1,y_1)$ and $(x_2, y_2)$, can $\rho^2$ be found for their union $(\{x_1 \cup x_2\}, \{y_1 \cup y_2\})$?

I have two sets of x-y coordinates: $(x_1,y_1)$ and $(x_2, y_2)$. I also have the $R^2$ value for each set of coordinates. (e.g. $(x_1,y_1)$ has the correlation coefficient of $R^2$) Given the stats ...
cracker_jack99's user avatar
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Difference between forecast, estimation, projection, prediction?

Could someone explain me the difference between those terms. For me all of them are somehow synonymous. Thanks in advance!
mathsdummie1234's user avatar
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Median definition

Definition 6.1.1 (Median): We say that $c$ is a median of a random variable $X$ if $\mathbb{P}(X≥m)≥ 1/2$ and $\mathbb{P}(X≤m)≥ 1/2$. (The simplest way this can happen is if the CDF of $X$ hits $1=2$ ...
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Physical interpretation of difference between joint frequency and singleton frequency

If $f(a, b)$ represents the frequency of features a and b occurring together and $f(a)$ and $f(b)$ represent the frequency of individual occurrences of features a and b, what does the term $f(a,b) - (...
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Conceptual Question on probability of tossing a coin problem as many as number of times

If we toss a coin as many as number of times , The probability of getting head or tail comes out to be almost half. I know this very well. But in real life scenario nobody is going to toss a coin 1000,...
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H-indeces as a measure of concentration of integers

Say we have $n$ integers, $x_{1}\leq x_{2}\leq\ldots\leq x_{n}$. For each $i\in\{1,\ldots,n\}$, we can find a unique integer $h_{i}$ as the "largest $h$ satisfying there are at least $h$ of $x_{...
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How do I use a chi squared test for homogeneity/other statistical method for this situation?

I am performing analysis on data of ~8,000 patients who have COVID. This is my scenario. I have information of each patient being classified as either severe or non-severe in how COVID-19 affected ...
mather123's user avatar
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Scaling by percentage - is this appropriate given this situation?

Let's say I have a range of formulations, and each formulation contains a different starting rate of water "x", and I want to test how fast the formula dries out over time (ie. loss of water ...
dustedcat's user avatar
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Median:Mean::Percentile:?

Here is a simple question that I am hoping has a simple answer. The median and mean are both estimates of the central tendency of a random variable. They both have different advantages in different ...
Mike Battaglia's user avatar
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Interpreting Gaussian measurements in terms of information theory

I have a quantity that I want to measure, and I have obtained three sets of measurements A, B, and C, each represented by their mean $\mu_A$, $\mu_B$, $\mu_C$, and standard deviation $\sigma_A$, $\...
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Modeling stability as trend in coefficient of variation - has this been done?

It seems to me that a trend of coefficient of variation (CV) values over time could indicate the stability of the measured quantity. For example, a CV that stays within a narrow band is more stable ...
Tristan Fabrini's user avatar
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Modeling angles and magnitudes using a bi-variate gaussian.

I have a bunch of points in n-d space who's coordinates follow a Normal distribution $(X=x_1,x_2,...,x_n\sim N(0,1) )$. The coordinates form an angle $\theta$ (with respect to some arbitrary vector $V$...
Liam F-A's user avatar
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grade of concentration for ones in binary sequences

We would like to have an index, say $I$, for the grade of concentration of ones in binary sequences of finite length $L$ and number $K$ of ones. Assume for simplicity that $L$ and $K$ are fixed, so we ...
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The equality of variance test

I am facing a strange problem, Imagine that you want to test whether the standard deviations of two populations are equal. Let us call the standard deviations of the first population $\sigma_1$ and ...
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What is the name for this function associated with Distribution Function?

Suppose a country where the distribution of income $Y$ is given by a Probability Density Function (PDF) that we call $f_Y(y)$, obviously: $$\int_0^\infty f_Y(y)\ \text{d}y = 1$$ The expected ...
user910130's user avatar
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2 answers
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Analogue for mean and spread of 2D lines [closed]

I have a set of 2D lines (contour lines from a collection of images), and would like to somehow represent them with an "average" and some measure of spread (se figure below). What could be a ...
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Curious about the way to calculate area of histogram rectangle

I have self-studied the book “Probability and Statistics for Engineering and the Sciences 9th Edition”. From the following paragraph (about histogram construction) on the page 17 This construction ...
Nishikawa Rin's user avatar
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How can I get the average value of a class A∩B knowing the average values of classes A and B?

I am trying to model the population density for my metropolitan region, but the published census data does not meet the precision requirements I need. The most accurate data I have avaiable are ...
Enzo Henry's user avatar
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Simulation study for a Exponential Distribution

I have a pdf defined as: $$f(x)=\lambda e^{-\lambda(x-b)}$$ Conduct a simulation study in R to explore the behaviour of the maximum likelihood estimator $λ_{MLE}$ for λ on simulated data $X_1, · · · , ...
Jay's user avatar
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Comparing sample mean of a month X to the distribution of points during month X last year

Let's say $M$ is a metric of interest in the context of time series. We are interested to see if the average $A$ of $M$ computed during month $M$ this year makes sense.I had many ideas: compare $A$ ...
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Possible criteria for considering a data point an outlier

Possible criteria for considering a data point an outlier. Given a data set, we can compute the 5 number summary: minimum, first quartile $Q_1$ (25th percentile), median (50th percentile), third ...
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Accurate interpretation of Lotka's law?

I am carrying out some research in which I am examining the research productivity of academicians in two specific fields of study using Lotka's law, which states: "The number of authors making n ...
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Is it reasonable to multiply the output of a model by a constant in an attempt to calibrate and better match real life data?

I'm trying to model the volume change of a lake. I've developed a rough mathematical model that somewhat matches the actual volume change of the lake. However, my model doesn't quite match exactly. ...
Zachary Kennedy's user avatar
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By comparing boxplots, how to tell which sample is more likely to have outliers?

For example, from three boxplots, like these how could I tell which one is more likely to have outliers? By outliers, I mean values below $Q1 - 1.5 * (Q3-Q1)$ or above $Q3 + 1.5 * (Q3-Q1)$
Jonas's user avatar
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Normality throught the time 2

Here is my problem (I have already spoke about it in another question but It is not the same question now): We observe data X(t) that depends on the time t. We make these observations at given times ...
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Isn't the appellation right-skewed for a function with positive skew backwards? What is the reason for this convention?

I have a very simple (and perhaps naive) question: Why do we call a ditribution "right skewed" (instead of left skewed) when it has positive skew, ie when the median/mean etc is $\textbf{ to ...
ThighCrush's user avatar
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How to determine whether a data set is symmetric or approximately symmetric

According to the textbook my lecturer is following, a set of data is "said to be symmetric about the value x0 if the frequencies of the values x0 − c and x0 + c are the same for all c. That is, ...
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Error as a single value to represent a set of data

Let's say I have a set of data which consist of Real Value, Approximation I, Approximation II. For instance, the data looks like this: Now, I'm not sure which error to choose so one can infer that ...
singularity's user avatar
1 vote
1 answer
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Probability of no vehicles in a given interval of time - KwaZulu Easter Holiday [closed]

I have a Question that I do not understand at all. If anyone can help it will be very much appreciated. In the early hours of Easter Friday, News24 reported that 300 vehicles per hour entered KwaZulu ...
Miane Oosthuizen's user avatar
1 vote
1 answer
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What is the equivalent of a z-statistic for a textual variable containing discrete values?

I have a variable in my data which contains discrete values which have no canonical order, e.g. Apple, Orange, Pear. These values appear with a certain frequency in ...
Simon's user avatar
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Is there a closed form of standard deviation of the min. entropy of a set?

Min. entropy $(H_{\infty})$of a set is defined as $ -\log_2(p_{max}) $ where $p_{max}$ is the highest probability of occurrence of any individual element of the set. There is also the $\chi^2$ ...
Paul Uszak's user avatar
1 vote
1 answer
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Is there a general definition of mean value that would include arithmetic, geometric and harmonic means as special cases?

It may not be necessary to have a general definition, but it does not seem as if it should be difficult to come up with one. One requirement might be that the mean of a set of numbers must always be ...
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logit and probit models

Basic background Hi, I'm relatively new to statistics and mathematics stack exchange so please bear with me. I'm trying to learn about the probit and logit models where the observables $y$ can only ...
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Estimating largest $k$ such that that norm([v1,v2,..,vk])<2 for random normalized vectors $v$

Suppose I sample $k$ vectors from normal distribution, centered at $0$ and with covariance $\Sigma$, then normalize them to have norm $=1$, and finally stack them as rows in a data matrix $X_k$. I'd ...
Yaroslav Bulatov's user avatar
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Dataset and its Quantitave Representation

I've been given the question: $$\mbox{Given the dataset, with 15 observations}$$ $$\left(4,55;\; 6,51;\; 3,04; \; 5,60;\; 3,69;\; 5,12;\; 7,31;\; 7,80;\; 8,31;\; 3,83;\; 4,44;\; 6,47;\; 6,14;\; 8;76;\;...
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