# 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.

400 questions
3answers
13k views

### Intuitive Way To Understand Principal Component Analysis

I know that this is meant to explain variance but the description on Wikipedia stinks and it is not clear how you can explain variance using this technique Can anyone explain it in a simple way?
10answers
7k views

### Why is variance squared?

The mean absolute deviation is: $$\dfrac{\sum_{i=1}^{n}|x_i-\bar x|}{n}$$ The variance is: $$\dfrac{\sum_{i=1}^{n}(x_i-\bar x)^2}{n-1}$$ So the mean deviation and the variance are ...
3answers
498 views

### How should a mathematically-inclined person learn descriptive statistics?

I am interested in learning descriptive statistics. But I am completely baffled, that there seem to be no mathematically rigorous books on this subject, as far as I know at least. The Wikipedia page ...
4answers
97 views

### $n$ vs $n-1$ for the standard deviation

Suppose that I went to Tasmania a few years before the "Tazie Tiger" (thylacine) became extinct. I sample say, $100$ thylacines and make some biometric measurements. To make the discussion concrete, ...
2answers
1k views

### How did Target figure out a teen girl was pregnant before her father did?

First of all I do not have a mathematics degree only a B.S. in finance so please take that into account when writing an answer. Generally what type of mathematics is involved here? And specifically ...
2answers
414 views

2answers
1k views

### Minimal sufficient statistic of $\operatorname{Uniform}(-\theta,\theta)$

I am seeking clarification on why both the vector $(X_{(1)},X_{(n)})^T$ and $\max\{-X_{(1)},X_{(n)}\}$ are sufficient for $\operatorname{Unif}(-\theta,\theta)$, but only $\max\{-X_{(1)},X_{(n)}\}$ is ...
1answer
70 views

### Problem related to the exact distribution and the CLT

I'm trying to solve a pretty straight forward problem but i can't find good info on the subjects necessary to solve it so i'm terribly stuck. I'll present it as follows and later try to explain my ...
3answers
45 views

### $E[\frac{1}{X}]$ 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 ...
2answers
211 views

### Unbiased estimator for $\theta$

Exercise : Let $X_1, \dots, X_n$ be a random sample $(n>1)$ from the distribution with pdf $f(x) = \theta x^{-2}, \; \; 0 < \theta \leq x < \infty$, where $\theta$ an unknown parameter. ...
1answer
48 views

### Prove that $\log[ ( x+\sigma)^a - (x-\sigma)^a ] = (a-1) \log(x) + C$

$\sigma>0$, $a>1$ and $C$ are constant real number. Does the following holds for any $x>\sigma$? $\log[ ( x+\sigma)^a - (x-\sigma)^a ] = (a-1) \log(x) + C$. Background John Tukey, on the ...
2answers
130 views

### Arithmetic mean is to addition as Harmonic mean is to …?

Take $n$ real numbers $x_1,\ldots,x_n.$ The Arithmetic mean $A_n=\frac{1}{n}(x_1+\ldots+x_n)$ is the answer to the question: "Which number, when added up $n$ times, is equal to the sum of the \$x_1,\...
1answer
2k views

### What qualifies as an infinite population?

I've been looking for a clear guideline to distinguish between a finite population and an infinite one, for example, in some places an infinite population is described as something like the number of ...
1answer
231 views

### Why minimising the MSE in Variance-Bias tradeoff?

As I understand the Variance-Bias tradeoff, modifying estimators to minimise bias might increase the variance of the estimator and vice-versa. For the simple case of the biased variance estimator, ...