For example, the "center" of a distribution is a ___

The sample mean is a measure of "center", and thus is not a ___

"Spread" is another ___

There are many measures of spread, e.g biased sample variance, biased sample standard deviation, IQR, etc.

Other ___ include skewness and kurtosis.

  • I don't understand what distinction you are trying to make. How can it be a statistical property if it isn't measured? – jxh Aug 2 '18 at 18:24
  • @jxh For example, center is a qualitative statistical property. It's roughly defined as "a value commonly seen" in a distribution, or "an expected value" of a distribution, but importantly, it has no description of exactly how to measure it. See en.wikipedia.org/wiki/Central_tendency. In that article, it also gives various measures of center: the arithmetic mean, the median, etc. Thus, there exists a very clear distinction between a vague statistical property, and a particular measure of that property. – extremeaxe5 Aug 2 '18 at 19:39
  • Qualitative means that it is a non-statistical non-property. It is just a descriptor being applied to a system that also happens to be amenable to statistical analysis. – Phil Sweet Aug 2 '18 at 21:30
  • Statistical distributions are models or theories proposed to describe facts about sets of observations. A distribution is characterized by certain parameters, such as the mean of a normal distribution. In fitting a distribution to facts, for instance, one might calculate an average in order to estimate the mean of the distribution. When an average serves this purpose, it is referred to as the "sample mean". – Greg Lee Aug 2 '18 at 22:08
  • Looking at this a bit more, descriptor might work as an answer. It shows up in the definition of Kurtosis, which is a measure of "tailedness". But I wouldn't consider any of your terms a property. They are concepts with which to compared things. The comparisons can be qualitative or quantitative. – Phil Sweet Aug 3 '18 at 2:40

As I understand the question, the OP is looking for a word that describes an aspect of variability but without prescribing any particular measure. So, if I am overweight I may be concerned about my shape, which cannot be measured, whereas my weight can be. My weight is a statistic; my shape is not.

One possible word is characteristic.

  • Everything can be measured. It is just a matter of a technique. For instance, you can poll people about a person's shape. – jxh Aug 2 '18 at 21:30
  • The point is to find a word for a quality without prescribing any particular measure. On the @jxh specific point about anything being measurable: it may be possible to attach a number to anything, but whether that truly measures it is a separate question. So, for example, does the sample mean actually measure the centre of a distribution? – JeremyC Aug 2 '18 at 21:36
  • The OP uses "statistical property". If there is no way to validate the correctness of the assertion, it is not appropriate to apply the term statistic to it. If there is a way to validate the assertion, then it is measurable. My answer allows for a person to make a guess as to what the measure might be without actually measuring yet. For centre, there would need to be a definition that makes sense to all parties, whether it is mean, median, mode, or something else (e.g., opinion poll). – jxh Aug 2 '18 at 22:35
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    @jxh I think you are being a bit naive. Fundamentally, we organize similar objects into classes. Most would agree that the measures we call ‘sample mean, sample median, sample mode,’ are “more similar,” than a measure like ‘sample variance.’ Now, a true fundamentalist would argue that no, there is nothing fundamentally more similar about these measures than any other, but I believe that this is a bit silly. So, what name do we give this class of measures? We call them “measures of center.” Similarly, IQR, sample variance, etc. are “measures of spread.” Now: what is “center”? – extremeaxe5 Aug 2 '18 at 23:52
  • @extremeaxe5: If you believe that there exist statistical properties that cannot be measured, then I would argue you are not actually interested in statistical properties. If you believe it is naive that testability is a pre-requisite for validation of an assertion, then I am happy to be called naive. – jxh Aug 3 '18 at 0:01

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