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—

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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?
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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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Is $50$th percentile equal to median?

Consider we have the $100$ distinct integers between $1$ and $100$ inclusive. The median and fiftyth percentile can be calculated as below. Ordering: $1,2,3 ..... ,98, 99, 100$ The median is $(50+51)/2$ The $50$th percentile is $51$ ($51$ is…
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…
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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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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…
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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:…
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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 what statistical formulas can be used in a scenario…
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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…
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What would one call the mean of the mean and median?

If we wanted to take the mean of the mean and median, what would we call that value? I'm considering this as a useful summary statistic with a heavily skewed distribution. For instance, if the mean of a distribution is 10 and the median is 15, the…
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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?
user248640
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Question about English sentences in statistics?

Can somebody help me interpreting the red circled sentences in planer English? I understand "We view $y_i$ as a realization of a random variable $Y_i$ that can take the values of one and zero" but the next following words, "with probabilities…
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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 $c$).…
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