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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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Statistical methods to compare 21 theoretical values to experiments

I am testing a theoretical model to compute an entity called the g-shift of diatomic molecules (the g-shift for a given diatomic molecule is expressed as a simple scalar value). I have calculated the ...
Manó's user avatar
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Uncertainties in measurements widen the normal distribution.

In redistricting (gerrymandering) analysis, a state is divided into districts where district vote shares are written in terms of one of two parties, so if district #1 has a vote share of 40%, it means ...
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Calculate contributions to the change of ratio a/b when be is the sum of a plus other variables

I would like to know how to calculate the change contribution to a ratio a/b where b is equal to a plus other variables: ...
Ayoze Alfageme's user avatar
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Average customer value

I have a table with customer purchase data. |customer | month | Purchase amount | number of days shopped | |A | jan | 200 | 5| |A | feb | 250 | 7| | A |...
Mpl's user avatar
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Unclear about the definition of "mutually exclusive"

Google says, "mutually exclusive is a statistical term describing two or more events that cannot happen simultaneously." But when we say that $n$ events are mutually exclusive, we mean that ...
Bob Marley's user avatar
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distribution of sample mean to sample standard deviation

Noting this question, it is known that the sum of squares of independent identically distributed gaussian random variables is a Noncentral chi-squared distribution. That is great and all, but what ...
Mefitico's user avatar
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2 answers
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Converting a multivariate linear correlation into a univariate one (predicting real estate prices in NY)

I am building a prediction model of real estate properties in New York based on a few inputs: Area (size) of the property Year it was built Number of bedrooms Number of parking spots The data is ...
bru1987's user avatar
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Weighted average value for five-point scale survey question

I have a survey question which has response choices on a 5-point scale. The response choices are: Not at all, Barely, A bit, Almost always, Completely. We've assigned a value to each response, ranging ...
Yellow Red's user avatar
2 votes
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How to estimate the best variance-proxy of a sub-Gaussian distribution from data?

Suppose we have $N$ independently identically distributed (i.i.d.) samples $X_1,\cdots,X_N$ generated from a sub-Gaussian random variable $X \sim \mathbb{P}$. Then by definition there exists the ...
Asce's user avatar
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Given a dataset of N values, how to calculate the position(index) of the value at x percentile

Problem is in the title. The formula usually given for this is: Required Index: $\frac{x}{100}\times (N+1)$ I don't understand how this is derived. why should it not instead be $\frac{Nx}{100}+1$ as $\...
LearningToCode's user avatar
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Incompatible results in finding the variance of random variable

Let $f(x) = 3/64(2x - 2)$ whenever $x \in [1, 5]$, zero otherwise, be the PDF of a random var. I know the expected value of $X$ is $2.75$. I was asked to find its variance. For the sake of practice I ...
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Which class will be the median class if n/2 is the cumulative frequency of a class interval?

An example problem: When using the textbook formula, Median = L + {[(n/2)-c.f.]/f}*h, where L is the lower limit of the median class, n is the total number of observations, c.f. is the cumulative ...
Curious 9th Grader's user avatar
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How can the Range be a measure of statistical dispersion?

Most of the sources (like 1, 2 3 and in some books like arihant) provide the definition for Statistical dispersion as " The extent to which numerical data is spread about the average value is ...
Altair25's user avatar
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Compare positive and negative percentages

I know that is a very, very trivial question... But I'd be super thankful for any help. Lets say you have three values where each describes the velocity of a car. 50 kmh, 100 kmh, 150 kmh I just want ...
Lenn's user avatar
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Is the sample mean absolute deviation unbiased for a normally distributed population?

Let $X_1,\ldots,X_n$ be a random sample from a normally distributed population. Is the sample mean average deviation $$\frac{\sum_{i=1}^n|X_i-\bar{X}|}{n}$$ an unbiased estimator of the population ...
ashpool's user avatar
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CDF of sum and subtraction of independent and identically distributed random variables having Gamma distribution with same shape and scale parameter

What is the CDF of the following: P$($$a_m$ $Z_m$ - $K$ $\sum^{M}_{i=m+1}$ $a_i$ $X_i$$ $<$ C$$)$ where $Z_m$ and $X_i$ are independent and identically distributed random variables, continuous ...
Math Explorer's user avatar
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Is quantile just quantile function evaluated at specific values?

According to Wikipedia, the quantile function is defined by $$Q(p)=\inf \{x\in\mathbb{R}:F(x)\geq p \}.$$ But if I apply this to equally likely data set 10, 11, 12, 13, I get $Q(0.5)=11$. But shouldn'...
ashpool's user avatar
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How do I develop an understanding of how equations were created? [closed]

Firstly: having a lot of difficulty figuring out how to articulate this question due to lack of general math knowledge. There are multiple questions posed below, but I feel like if I knew more they ...
A L's user avatar
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Consistency OLS without intercept

I have this model without intercept $y_i = \beta x_i + u_i$ where $\widehat{\beta} = \frac{\sum x_i y_i}{\sum x_i^2} = \beta + \frac{\sum x_i u_i}{\sum x_i^2}$ I want to verify the consistency of $\...
Constanza Zepeda's user avatar
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What is the name of the function which results from sampling a sigmoid?

It is not just two Gaussian distributions. I would hope that it is defined and has a name, but I can't find it. I would love to know more about it (parametric formula, how to extract the parameters ...
pnda's user avatar
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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 ...
Coder's user avatar
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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 ...
Bulworth's user avatar
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47 views

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-...
Greg's user avatar
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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 ...
Squirtle's user avatar
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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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448 views

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)....
Joe's user avatar
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1 answer
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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 + ||\...
Alberto's user avatar
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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 ...
Willy's user avatar
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1 answer
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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, ...
Jose_Peeterson's user avatar
23 votes
4 answers
2k views

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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29 views

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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13 views

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 ...
Davide Barcella's user avatar
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1 answer
608 views

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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35 views

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 $1=2$ ...
Saif's user avatar
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1 answer
25 views

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) - (...
kauray's user avatar
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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,...
Akash's user avatar
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1 vote
0 answers
36 views

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_{...
Q9y5's user avatar
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1 vote
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53 views

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
1 vote
0 answers
48 views

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
2 votes
0 answers
36 views

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 $\sigma_A$, $\...
Marco'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
1 vote
1 answer
32 views

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 ...
Davius's user avatar
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2 answers
65 views

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 ...
blupp's user avatar
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1 vote
2 answers
71 views

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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41 views

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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1 answer
115 views

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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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 ...
lulufofo's user avatar
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