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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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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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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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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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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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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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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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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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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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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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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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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
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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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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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40 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
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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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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 ...
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1answer
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Existence of distribution for a Moment Generating Function

Question : Does a distribution exist for which $M_X(t)=\frac{t}{(1-t)},|t|<1 ? \text{ If yes, find it. If no, Prove it.}$ Answer : Since the mgf is defined as $M_X(t)=\mathbb{E}e^{tX}$, We ...
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Use samples to estimate standard deviation

The followings are independent samples from two normal populations. Both of which have the same standard deviation. 16, 17, 19, 20, 18 and 3, 4, 8 How to estimate standard deviation?
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Showing that the Lasso solution path is linear as $\lambda$ ranges

Consider Lasso problem with the Lasso parameter $\lambda$. Suppose that the set of active predictors is unchanged for $\lambda_0 \geq \lambda \geq \lambda_1$. Show that there is a vector $\gamma_0$ ...
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Intuitive explanation of the formula for mode (grouped data).

The formula for finding the mode in grouped data is given by: $$ mode = l + \frac {f_1 - f_0}{2 f_1 - f_0 - f_2} X h $$ where, l = the lower limit of the modal class, $ f_1 $ = the frequency of ...
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Deriving the corresponding Location - Scale Family

I am little confused about deriving the location-scale family of these three distributions. (a) Let $f(x)=\frac{1}{\pi (1+x^2)}$, $-\infty<x<\infty$. I have no idea how to go about this. (b) ...
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Correction factor for calculating standard error when drawing sample without replacement - derivation

When drawing a sample of size n from population of size N This relationship holds $$ SE\space when\space drawing\space sample\space without\space replacement\space =\space correction\space ...
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1answer
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How to find a new average?

The average time spent on Facebook per day of 40 students in a Statistics class is 1.4 hours, while the average of the 32 students in the Calculus class across the hall is 1.9 hours. Two students from ...
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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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1answer
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Finding the sample size given bound of error and standard deviation.

The personnel manager wants to determine if there is a difference in the average time lost due to absenteeism between two plants. From historical data, the estimated standard deviations of lost time ...
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How to tell which groups have different means than others in a One-way Anova

The presence of harmful insects in farm fields is detected by erecting boards covered with a sticky material and then examining the insects trapped on the board. To investigate which colors are most ...