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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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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 ...
2
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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 ...
5
votes
2answers
144 views

How can the median number of sexual partners be 6.1 and 3.6?

http://www.cdc.gov/nchs/nsfg/key_statistics/n.htm Median number of female sexual partners in lifetime, for men 25-44 years of age, 2006-2008: 6.1 Wouldn't it only be able to be x.5 or x.0?
1
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1answer
704 views

Interpreting the scatter plots of two random variables

Suppose I sample random variables A and B from normal distributions. When I do a scatter plot of these two variables I see a ...
0
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1answer
809 views

Correctness of a statistical evaluation of a parameter

I have a question about a non-Gaussian distributed parameter that can only take certain values in a defined interval. Knowing that I have to define this parameter starting from a set of its values and ...
3
votes
1answer
73 views

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 ...
0
votes
0answers
156 views

'Weighted' Markov Chain Statistics

Let $\mathbf{X} = (X_0, X_1, ..., X_n)$ be a finite length walk on a Markov chain with initial distribution $\lambda$, transition matrix $P$, over the state space $\Omega = \{1, 2, ..., l\}$. Suppose ...
2
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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, ...
2
votes
1answer
932 views

What is Expected Prediction Error (EPE) a function of?

Context I am self-studying Elements of Statistical Learning (2nd ed), by Friedman, Hastie & Tibshirani. I have a question with regards to what the EPE, as defined in this text, is a function of. ...
2
votes
1answer
124 views

Which mean is used for standard error?

While calculating the standard error, we take the standard deviation of the sampling distribution. But for calculating the standard deviation we must consider a 'mean' to take difference about. In ...
1
vote
1answer
840 views

MLE of variance minimising the mean squared error

While reading up on the derivation of a Maximum Likelihood Estimator for population variance, the MLE for Variance ends up being the biased sample variance, $\frac{n-1}{n}S^2$ where $S^2$ is the ...
1
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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 ...
1
vote
1answer
548 views

Measure dispersion of a set of values resides in a range

I want to know what is best method to calculate (measure) the statistical dispersion of a set of values resides between a range. Scenario: My goal is to build an index. I have two methods that ...