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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choosing an index for points given to playoff teams [closed]

Short brief:I am doing a project about the correlation of the success of teams(for example) in champions league and their revenues. I want to build a linear regression for example based on the success....
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Variational Inference for Item Response Models Estimation

I should work on a project about Variational Inference for Item Response Models Estimation. This is my university project but I don´t find relevant information around this topic so I would be very ...
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Calculating 'acceptable' % change month over month

We are tracking a set of monthly business metrics (some are absolute numbers and some are %). For each metric, we want to find a range of variations that tells us if the current month's performance is ...
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How do we standardize data for higher moments?

I know that if I want to transform some data points to a mean of zero and standard deviation to 1 I can use this formula: $$Z= \frac{x-μ}{σ}$$ However if for example I want for example to normalize my ...
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40 students each throw a fair die 12 times [closed]

40 students each throw a fair die 12 times. Each student then records the number of times that a six occurred in their own 12 throws. The student monitor then calculates the average number of sixes ...
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How to measure the ranking deviation of a matrix of elements

I have elements in a table as seen here: Experiments 1st place 2nd place 3rd place 4th place 5th place 1st run Element20 Element23 Element10 Element13 Element0 2nd run Element23 Element27 Element10 ...
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Why do these two derivations of the variance of a binomial random variable give different answers?

I am learning AP Statistics, and I have come across the derivation for the variance of a binomial random variable. The derivation goes something like this: Suppose you have a binomial random variable $...
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Statistical method for assessing experimental and theoretical errors.

Let us suppose I have performed an experiment where the mean value is given by $V^{\rm exp}$ and its std is estimated as $\sigma_{V^{\rm exp}}$. Now, let us also suppose that theoretically, I am ...
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calculating weekly occupancy given daily capacity and booking

I aim to model weekly room occupancy as percentage but observe a very "bipolar" (?) distribution (majority of rooms either have 0% or 100% occupancy). This made me wonder, if I possibly do ...
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Why are these numbers are an inferential and a descriptive statistic?

A 2005 newspaper article states that "The highway fatality rate sank to a record low last year, the government estimated. But the overall number of traffic deaths increased slightly. Overall, ...
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Sample variance update formula

For the following formula for the update of the sample variance: $$S_{k+1}^{2}=\left(1-\frac{1}{k}\right) S_{k}^{2}+(k+1)\left(\bar{X}_{k+1}-\bar{X}_{k}\right)^{2}$$ is there a way to make prove it? ...
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Inference Statistics to prove that during Financial Crisis of 2007-2008, the gdp of US, UK, Japan, France have fallen down.

I am working to do some analysis on the GDP data of different countries. By, time series plot i.e. Year Vs GDP I can easily prove that during the financial crisis of 2007 - 2008, the GDP of the above-...
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Compute $Var[\frac{1}{n}\sum_{i=1}^n (X_i-E[X])^2]$

Let $X_1,\ldots, X_n$ be positive random variables in the range $[a, b]$ and $\sum_i^n X_i = 1$. I want to compute \begin{eqnarray} Var[\frac{1}{n}\sum_{i=1}^n (X_i-E[X])^2] &=& \frac{1}{n^2}...
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Association of Categorical and Qualitative Variables

I am trying to look at the association between the cost of goods depending on the area. Group A bought their product in one area and group B bought theirs in another. Group A is larger but group B is ...
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double summation with adding and removing bar X

I need help with this please: we have from other question (question 1) $$Sxx=\sum_{i=1}^n (x_i-\bar X)^2=\sum_{i=1}^nx_i²-n\bar X=\sum_{i=1}^nx_i(x_i-\bar X)$$ And we have to transform this: $$\sum_{...
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Estimative for parameter with method of moments and maximum likelihood

Given an random sample $X$ ~ $F_{\theta}$ such that $F_{\theta}$ = ${(\theta}^x)(1-{\theta})^{(1-x)}$ if $x\in {{0 ,1}}$ and $\theta$ belongs to the interval 0,1 Consider the data following data ...
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Dynamic Data Normalisation

I am facing an issue to compare dynamic data. The situation is something like this as described below. Suppose I have $n$ students in a class and I take an exam that was very tough and since the ...
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What is sampling bias?

From the definitions I've read online they all go something like this... Sampling bias occurs when some members of a population are systematically more likely to be selected in a sample than others. ...
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What are the limitations of this study?-

I am tackling the study of the company, where I know that: A financial firm is interested in the impact that caffeine has on an employee’s sleeping patterns. Participants are allocated to either ...
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1 answer
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Which test to use when I have population data?

Population Data I have a large dataset of funds to all the training schools in London. It's a complete dataset i.e. it represents the population I am studying. I only want to know about the training ...
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How to compute for standard deviation in this problem?

The local administration installed 3500 Incandescent bulbs as part of a new lighting system project. According to them, the bulbs are produced by several companies and have a burn time of 1060 hours ...
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Probability from study that analyzed the relationship between smoking in parents and the incidence of pneumonia and/or bronchitis

I need help understanding this probability exercise. In 1974 Colley et al. published a study that analyzed the relationship between smoking in parents and the incidence of pneumonia and/or bronchitis ...
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Legitimity of a "gaussian approximation" for a qualitative-values bar chart

Sorry per advance if my question is not in the right place but I couldn't find a statistics-dedicated Stack Overflow site. Anyway, here is my problem: One friend of mine is currently writing her phD ...
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How to statistically describe this set?

Imagine I want to statistically characterise a set of converging points and still get an idea of the converging properties or shape of such set, for example The values of the mean or variance of the $...
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Statistical Analysis of Ranked Data

would be eternally grateful for some helps with my question ... Yes, I'm a noob ... I've been tasked with analyzing the below Data - the problem is that I'm essentially a programmer as opposed to a ...
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What can be the upper bound of the deviatons in a data set, given the mean and the SD? [duplicate]

Let $X$ be a set of $n$ numbers with the mean $m$ and the SD $\sigma$. Let the maximum deviation $$D=max\{|x-m|:x\in X\}$$. Then $$D^2/n\leq\sigma^2$$ so $$D\leq\sqrt{n}\sigma$$ is an upper bound of $...
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Find PDF and Join probability density function of a set of points

I have a set of data points for three random variables: $x_1 = \{4.5, 4.3, 5.1, 5.2, 4.8,5.1, 5.3,5.6\}, x_2 =\{3.5, 4.5, 4.1, 5.1,4.9,4.6,5.2,4.8\}$ and $x_3 = \{7.4, 6.8, 6.6, 7.8, 8.2. 7.8, 7.8, 8....
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Are the summed medians of m datasets the median of the summed dataset?

We have m datasets of n elements, where each element represents the grade of a student (from 1 to 10) for a given test. We are told that student Peter always achieves a test score that is the median ...
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How is the "precision matrix" derived from the covariance matrix?

The probability density function (PDF) of a Gaussian (or Normal) distribution centred on the origin in n-dimensional space is given by : p($x$) = B exp[$-\frac{1}{2}x^T\Lambda x$], where $x = (x_1, ......
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Comparing a two different sequences of values to a third, correct sequence, and determining which of the two is more accurate.

I have a question in mind and would be thankful for any help: Consider some values: $a_1, a_2, \cdots, a_n$. Assume that these values are the true, correct values. Now consider two other sets of ...
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Probability of landing heads following a normal distribution

The following is a question which I personally find badly constructed, and would like to gather some opinion on: Suppose you select a coin from a pile that is thought to have probability of landing ...
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Relation between median and arithmetic mean

The median of the numbers in a list is $x$, and the arithmetic mean of the numbers in the list is $\frac{x+1}2$. Quantity $A = x$ and Quantity $B= \frac{x+1}2$ Quantity $A$ is greater. Quantity $B$ ...
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Restricted regression model with insignificant variables being = 0

Okay so, i have a regression model : $PRMRES_i=β_0+β_1 OMS_i+β_2 KONK_i+β_3 NYPR_i+β_4(NYPR_i×OMS_i) +u_i$ Where PRMRES is operating profits, NYPR is dummy variable, indicating if one or more of the ...
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Understanding Decile [closed]

I was checking a Linkedin profile and I came across this statement in the “Grade” section. It’s a little confusing. It is as follows: From the picture above, the statement in Spanish translates as: “...
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Calculate variance from average age when there are many of the same age?

I want to calculate the standard deviation of a region of people aged 18 to 26. I have got the mean by multiplying the age by the frequency and dividing it by the total frequencies of all ages. (Mean ...
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How to prove the independence of the functions of two random variables distributed with multivariate normal. [duplicate]

I have to prove this statement on one of my problem sets: If X1 and X2 are independent random variables, both distributed as N (0,1), then X1+X2 and X1−X2 are independent random variables. I know that ...
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Determing Sample Size need with Binomial Distribution

Trying to learn how to use this equation. The author of the paper list example numbers and the answer. Can someone show me a few steps into the problem. I'm getting $r=0$, $r=1$, but can't seem to ...
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1 vote
1 answer
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summations with unusual notation,as interpreted?

I have seen here and in many places summations that do not follow a standard notation, I put some of them below: For example how to interpret these. Some bibliography with this type of notation? I can'...
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Calculating the probabilities given the expected value and weights in a game of chance

Suppose you've got a game wheel that can be divided into m slices where each slice contains a symbol and an associated multiplier w. The game is played by placing bets on one or more symbols where the ...
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What kind of function can model a distribution that is strictly positive and skewed right?

Start with $\text{global minimum}=0, \text{target}=:\text{mean}=\bar{x}, \text{global maximum}→\text{infinity}$ corresponding to a smooth continuous probability distribution of $x$. Now suppose that ...
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Correlation between margin of error and sample size

Consider the following situation: Margin of error = 2% C-interval = 95% Why is it that you require less sample size to produce the same margin of error in a c-interval when you have a lower prob. of ...
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2 votes
2 answers
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Two types of averages for ratios of two things

It was brought to my attention in this video that, where you have some attribute of your data that is the ratio of two other attributes, there are two ways of generating the mean "average" ...
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1 vote
1 answer
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Sampling from a 2D to 1D distribution

I have one question/problem regarding sampling and I am not sure in which category this falls (it looks like bootstrapping) Let's say that I have some real surface $z = f(x, y)$ on some bounded domain ...
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1 vote
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Unbiased estimator for variance when each $x_i$ has probability $p_i$

Suppose we have a sample of 3 "observations" $x_0, x_1, x_2$ from a PMF of unknown mean, where we know that each observation $x_i$ has probability $p_i$. Then a biased estimator of the mean ...
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skewness and kurtosis of the sum and difference of correlated random variables

In the same way that the variance of the sum (or difference) of correlated variables can be determined (e.g. see here - https://en.wikipedia.org/wiki/Variance#Sum_of_correlated_variables) is there an ...
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Conditional Probability given Joint density Function

Let X and Y be continuous random variables with joint density function $f(x,y)=24xy$ on the domain $x,y>0, 0<x+y<1$ and is $0$ otherwise What is the conditional probability? $$P(X>1/2 | X+...
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Are median and mode also 'moments' of a probability distribution?

Wikipedia describes 'moments' as quantitative measures related to the shape of a function's/distribution's graph. In that case, are median and mode also essentially a form of moments? If not, why not?
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Understanding variance formula

I know that $var(X)=E[(X-E(X))^2]$ . However, I am confused because it seems to me that this definition is recursive in that the expected value of the square is itself a function of an expected value. ...
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Student's $t_\nu$ distribution [closed]

Can anyone help me to solve the exercise $(4.6.9)$ from Nitis Mukhopadyay book ? I do not know even how to begin the transformation technique suggested. I'm interested in the derivation of $(11.4.11)$...
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How to solve this median problem?

If a distribution of data has median $m$, what are the data that can be added to the distribution and allow the median value to be preserved? It is clear to me that there are two cases: a) Odd case $(...
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