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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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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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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 ...
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How does inverting data change standard deviation?

This seems like such a straightforward question but, after googling the title of this question and variations thereof, I haven't been able to find an answer. Please point me in the right direction if ...
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Conditional probability question about children

Sushma has $2$ children. Let $A$ be the event that the oldest child is a girl, $B$ be the event that at least one child is a girl, and $C$ be the event that both children are girls. Which of the ...
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Yule's coefficient of association

If with usual notations for two attributes the inequality (AB)(αβ)<(Aβ)(αB) holds, then -1 ≤ Q ≤1 is true? According to me the answer is false because in the given condition either A or B are ...
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Yule's Coefficient condition

If with usual notations for two attributes the inequality $(AB)(\alpha\beta)<(A\beta)(\alpha B)$ holds, then $-1 \leq Q \leq 1$ is true. According to me the answer is false because in the given ...
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63 views

Value of Correlation coefficient

Suppose a computer has found for a given set of values of X1, X2 and X3: r12=0.90, r13=0.30 and r23=0.70. Examine whether these computations are error free. I used partial correlation coefficient to ...
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boxplot analysis

Similar boxplots with different quantity of outliers I have boxplots (shown on picture) and in my homework I should decide which statement about them is right. They are: 1) 1st set - fewer outliers ...
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Estimating population size of endangered parrots

I am trying to find the best way to analyse the results of a study I have just coordinated. In short, I want to be able to estimate the total population size of a species of parrot based on ...
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34 views

Independence of sample mean and sample variance

It is well known that under normality assumption, the sample mean and sample variance are independent, by Basu's Theorem. My question is that, is the normal distribution the only distribution whose ...
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2answers
143 views

Real Examples of Misleading Statistics

I need to give a presentation to a group of students on Tuesday about why one needs to be careful when examining statistics or mathematical results in the media or online. In his book How Not To Be ...
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How to graphically visualize how well a copula fits a sample of pseudo observations?

I have a bivariate data sample $(a, b)$ which I would like to model with a joint distribution $(A, B)$. I fitted the marginal distributions for $A$ and $B$, however, the samples $a$ and $b$ are not ...
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Express $x_{n+1}$ in terms of $n,\bar{x},s^2$.

Consider a set of $n$ observations {$x_1,...x_n$}, with mean $\bar{x}$ and variance $s^2$.When a new observation $x_{n+1}$ is added to this set,the mean decreases,but the variance remains the same....
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How may a bivariate and univariate hypothesis test be useful for this data set?

If anyone can assist, I'll greatly appreciate it So my main research question is on government views (if people approve or disapprove of the government) and it's relationship to education policy (...
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2answers
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The “correct” standard deviation

This may end up being a question more about scientific best practice than anything else, but I think this is the right community to ask it in to get the insight I'm looking for. Say I have two little ...
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1answer
24 views

How do I prove the combining of errors with the following formula?

I am given that $\text{var}(h) = \sum_{i=1}^k (\frac{\partial h}{\partial X_i})^2 \ \sigma_i^2$ and with this I need to prove that: $\sigma(X+Y) = \sqrt{\sigma_x^2 + \sigma_y^2}$ $\lambda$ = $\frac{...
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Why find the inflection points on a bell curve?

I understand that the inflection points on a standard normal curve can be calculated with the equation $\mu \pm \sigma$, or essentially where z = $\pm$1. I don't fully understand the significance of ...
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Two population hypothesis test sample size

A retailer is trying a new concept in 3 of its 200 stores. The trial period is 10 weeks. The goal is to increse sales with at least 10%. The tricky part is that there is sesonality and campaigns that ...
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Physical interpretation of taboo probability

We know that in a Markov chain the taboo probability, $P^n_{i,i+1}(H)=Pr\{ X_n=i+1,X_k$ doesn't belong to $H$ for $0 < k < n| X_0=i \}$, where $H$ is an arbitrary set of states in a Markov ...
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2answers
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Suppose that a statistical model is given by the family of Bernoulli($\theta$) distributions where $θ \in \Omega = [0, 1]$. Calculate $\psi(\theta)$

Suppose that a statistical model is given by the family of Bernoulli($\theta$) distributions where $θ \in \Omega = [0, 1]$. If our interest is in making inferences about the probability that two ...
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2answers
20 views

Calculating sample variance

Suppose the following data are obtained by recording $X$, the number of customers that arrive at an automatic banking machine during $15$ successive one-minute time intervals. ...
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finding the mean and variance descriptive statistics

Suppose the following data are obtained by recording $X$, the number of customers that arrive at an automatic banking machine during $15$ successive one-minute time intervals. Q) Record the mean and ...
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3answers
38 views

Methods to estimate a probability distribution from truncated data?

I have a large set of values $t = \{t_i\}_{i=1}^N$. In actuality, these values (in some set of units) can range between $0$ and an unknown cutoff of the order of $10^7$, but they come from a numerical ...
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1answer
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Calculating Error Bars for Multiple Readings

[NOTE]: I am relatively new to statistics and attempting to gain a basic ground on the subject. For my question, I was curious how one could calculate the range for an error bar if the data point in ...
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Question on definition of unbiased estimator

The definition in my textbook is the following. Let $\big(\Omega, \mathcal{F}, (P_\vartheta:\vartheta\in\Theta)\big)$ be a statistical model and $(E,\mathcal{E})$ be a measurable space. If $E$ is a ...
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Problem on the Interpretation of Specfic Regression Equation Variables

This is a problem on interpretation of regression equations which have categorical explanatory variables where slopes on non-categorical variables do not depend on the category. This model assumes ...
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Significance testing difference in two changes of NPS. Significance of difference, NOT NPS itself.

I'm trying to calculate if the difference between two NPS changes is significant. For clarity: I have groups $a$ and $b$; group $a$'s NPS increased by $20$, group $b$'s NPS increased by $10$, so the ...
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21 views

Mean and median of a distribution

One study mentions that they found over 90% of the nation's school districts reported that their students were scoring "above the national average." Explain why this report is incorrect. Does the ...
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1answer
45 views

Computing the overall mean value in a game of chance with related means

Suppose you are presented with the following game: Game Interface How the game works: Player places bets on one or more symbols. The wheel is spun. If the wheel lands on a symbol that the player ...
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1answer
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Is there any meaning of this “Median-mean”

Given a data set $\{a_1,\cdots,a_n\}$ with median M Define the medimean to be the value of $x$ s.t. $$\left(\frac{1}{n}\sum_{n}{}{a_n}^x \right)^{1/x}=M$$ Is this $x$ value useful / used at all in ...
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1answer
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Normalize descriptive stats for comparison

I hope it is not a trivial question. I have data for a machine learning experiment from 2012 to 2018. In 2012, the samples are far different from the ones of 2018. Each sample is a little ...
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2answers
26 views

Understanding percentile computation

I understand percentile in the context of test scores with many examples (eg. you SAT score falls in the 99th percentile), but I am not sure I understand percentile in the following context and what ...
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Statistics on life expectancies

I don't understand how to solve the last the questions of this problem. Can anybody help me with this. [The table shows the life expectancies of a child (at birth) in the United States for selected ...
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1answer
39 views

Find optimal Bayesian decision based on a criterion for the posterior mean

I recently ran into the following exercise when practicing for an exam I have about Statistical Inference. The question looks very large and complex and I'm wondering if this is actually true or if it ...
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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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26 views

Producing a range of 0-100 based on multiple variables with different units (percent, numerical)

I'm absolutely no statistics wizard and it is my first post here, so I hope you bear with me. I'm working in Excel on a project where I need to convert data from a number of variables into a "one ...
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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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1answer
38 views

change detection formula most suited to analyse 3 vector changes

The following data is captured from the magnetic sensor of a device. This data has a time factor. The device is at times in motion and other times still How can one detect (using formula) if there ...
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1answer
42 views

$\operatorname{Var}[\sum_{i=1}^n (X_i-\mu_0)^2]=\operatorname{Var}[ \sum_{i=1}^n(X_i-\overline{X})^2]$?

Consider independent $X_1,\ldots, X_n\sim\mathcal{N}(\mu_0,\sigma^2)$ with a known $\mu_0\in\mathbb{R}$ and unknown $\sigma^2\in(0,\infty)$. I already know that $$\DeclareMathOperator{\Var}{Var}\...
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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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Long Range Dependence, Order Statistics

I have a long range dependence process which is defined in such a way: $$σ^2_{μ,X}=∫_T∫_{R^2}Cov_X(t,u,v) μ(du) μ(dv) dt. $$ We can use derived formula for covariation using distribution functions ...
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CHI squared test with probability

I'm facing a doubt: supose a group of 100 persons that die after a certain event. From those 100 persons, 77 are women, and 23 men. How do I test (with chi-squared) if the cause is related to the ...
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2answers
251 views

Matrix calculus for statistics

I want to calculate the variance of a sum of random variables $ (X_1+X_2) $. Doing statistics, I have to learn maths starting from the end and it is quite difficult, yet very interesting (please ...
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Why do we find central tendencies tendencies for grouped frequency data?

When data is grouped, it does not give the exact values of the frequencies of the observations. Then how do we calculate the Central Tendencies of the data? Our school text books give us some formulas....
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141 views

Exponential family for Gumbel distribution

Consider the Gumbel distributions $(P_\vartheta)_{\vartheta\in\theta}=(G(\beta,\mu))_{(\beta,\mu)\in(0,\infty)\times\mathbb{R}}$ with distribution functions $$F_{\beta,\mu}(x)=e^{-e^{-\frac{1}{\beta}(...
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3answers
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$E[\frac{1}{X}]$ for $X\sim\Gamma(n,\theta)$

Consider iid random varibales $(X_i)_{1\le i\le n}$ with $X_i\sim Exp(\theta)$ for $1\le i\le n$ and $\theta\in(0,\infty)$. Then we have $$\sum_{i=1}^nX_i\sim \Gamma(n,\theta)$$ with density function ...
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Probability and Statistic

I have a question about how to calculate the confidence interval. The problem is: I have a model which gives the probabilities of 4 genotypes AB, Ab, aB and ab as (1/4)(2 + theta), (1/4)(1 - theta), (...
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1answer
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How to draw a boxplot with whiskers correctly?

I want to draw a boxplot with whiskers where a lower bound is equal to $Q1 - 1.5 IQR$ and an upper bound is equal to $Q3 + 1.5 IQR$, where $Q1$ is a lower quantile, $Q3$ is an upper quantile and $IQR$ ...
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What is the meaning of this Symbol $E$

I was going through this excellent article on GANs and WGANs Here While going throught the Discriminator Network's mathematical semantics, I came across this symbol : $$E_{x \tilde {p_{r(x)}} } [\...
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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 ...