Mathematics Stack Exchange
Mathematics Stack Exchange

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.

Descriptive statistics is the process of using and analyzing statistics that quantitatively describe or summarize features of a collection of information.

Descriptive statistics is distinguished from in that descriptive statistics aims to summarize sampled data rather than use the data to learn about the population that the sample of data represents. Hence, descriptive statistics, unlike inferential statistics, is not developed on the basis of probability theory.

Measures used to describe a data set include—

581 questions
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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 measuring the same thing, yet variance requires squaring the…
Emi Matro
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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?
Jack Kada
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Why is the geometric mean less sensitive to outliers than the arithmetic mean?

It’s well known that the geometric mean of a set of positive numbers is less sensitive to outliers than the arithmetic mean. It’s easy to see this by example, but is there a deeper theoretical reason for this? How would I go about “proving” that…
TheProofIsTrivium
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Strange distribution of movie ratings

I like math but I also like movies. I have been collecting movies all my life. My collection is rather huge: almost 25.000 movies. Being also a developer I was able to create my own online catalogue and pull various statistics from the database.…
Oldboy
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Is $50$th percentile equal to median?

Consider we have the $100$ distinct integers between $1$ and $100$ inclusive. The median and fiftieth percentile can be calculated as follows: Data set: $1,2,3 ..... ,98, 99, 100$ The median is $(50+51)/2 = 50.5$ The $50$th percentile is $51$…
Cardinal
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$n$ 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, let's make the data the skull widths at the widest…
Barry Stone
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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 states, that descriptive statistics is not based…
Stefan Perko
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How can the Central Limit Theorem apply to Finite Populations?

In my statistics for beginners course we've just been introduced to the CLT, where it's been stated that a distribution of sample means tends to the normal dist. as your sample size $n$ increases to infinity. But what if your population is finite…
TheRealPaulMcCartney
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Why is it called the "sampling distribution of the mean"?

Is there a good (or even a bad) reason why it's called the "sampling distribution of the mean" and not the "distribution of the sample mean"? If we take multiple samples all of the same size, $n$, we get a distribution of sample means, $\bar{X}$. If…
Jeff
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How to transform/shift the mean and standard deviation of a normal distribution?

Given some Gaussian distribution with mean x and deviation s, how do I transform the distribution to have a new specific mean and specific deviation. Say the distribution has a mean, $\bar x = 4$ and deviation, $s = 10$, and needs to be transformed…
sam
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Intuition for Standard Deviation

I've been studying descriptive statistics and am having a hard time understanding the actual intuition behind standard deviation. I'm trying to get a practical feeling for it and so I'm trying to draw conclusions from it using a distribution of 20…
Danilo Souza Morães
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Canonical probability distribution associated with the "harmonic mean"

Is there a canonical continuous probability distribution, the center of which is best characterized with the harmonic mean, given by $$ \mathrm{HM}(X) = n \cdot \left( \sum\limits_{k=1}^{n} x_k^{-1} \right)^{-1}? $$ With "canonical" I mean:…
Björn Friedrich
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Definition of a percentile

I recently began a study of Introductory Statistics by Sheldon Ross. In the book, he defined a percentile as follows: The sample $100p$ percentile is that data value having the property that at least $100p$ percent of the data are less than or…
Toba
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Generalizing the mode and mean like the quantile

The mode, median, and means of a series of number ($x_1,x_2,...,x_N$) can be roughly thought of as the points that minimize the $p$-norm of the sequence for $p\in \{0,1,2\}$. The median is $c=\min_c\sum_i^N |x_i-c|^1$ (ignoring uniqueness of $c$).…
BeingQuisitive
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Regression to the mean - a simple question

In my statistics book there is a following question: In studies dating back over 100 years, it's well established that regression toward the mean occurs between the heights of fathers and the heights of their adult sons. Indicate whether the…
Ali Jarbawi
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