# Averages and Standard Deviations, but Skewness and Kurtosis?

Suppose I explain the following table in my academic paper.

``````State     Average   St. Dev.  Skewness  Kurtosis  Fis. Info.
CA        1.23      4.56      1.35      2.46      1.47
NY        4.56      7.89      7.91      8.02      2.58
TX        7.89      1.23      3.57      4.68      3.69
``````

The table displays the averages, standard deviations, skewness (?), kurtosis (?), and Fisher information (?) of the states.

(1) I couldn’t find both skewness and kurtosis in Cambridge Dictionary, but it seems they are abstract nouns and uncountable. I used averages and standard deviations above as they’re countable and each column has three numbers. Should I use skewness and kurtosis, or skewnesses and kurtosises?

(2) Fisher information is another statistic as well. Though there are three numbers in the last column, I can’t use Fisher informations as information is uncountable. Despite of the three numbers, should I still just use the Fisher information alongside the averages and standard deviations?

(3) Volatility is uncountable according to Cambridge Dictionary. Suppose there are historical volatility and implied volatility in my paper. Should I use historical and implied volatility, or historical and implied volatilities?

(4) I have multiple implied volatility observations (for example, 0.47, 0.13, 1.42, etc.) in my data set. Should I still use the volatility and avoid the volatilities though there are multiple numbers?

The division between countable and uncountable nouns is not so strict and arbitrary for abstract nouns as you seem to have learned. When an abstract noun refers to a specific measurable quantity or quality, it is often possible to pluralize it, even if the noun normally is not used in the plural form.

“Volatilities” is not an impossible form; you can see it used in a 2004 book by David Ruppert:

The implied volatilities vary among themselves.

Similarly, plural forms of “-ness” nouns, such as “skewnesses”, can be used in this kind of context, as shown by this quote from “Robustness in ANOVA”, by Rand Wilcox:

If the skewnesses corresponding to the two groups are identical,

(Applied Analysis of Variance in Behavioral Science, 1993, edited by Lynne Edwards, p. 350)

That said, “informations” does sound strange to me even in this context. (I think it’s because “information”, unlike “volatility” and “skewness”, is not treated in ordinary speech as a noun that refers to a quality of something.)

If pluralized, “kurtosis” would most likely turn into “kurtoses” /kəɹˈtoʊsiːz/ rather than “kurtosises”. Nouns ending in -sis, which mainly come from Greek, generally pluralize by replacing -sis /sɪs/ with -ses /siːz/.

You can avoid the use of any plural forms by using a phrasing like “The table displays the average, standard deviation, skewness, kurtosis, and Fisher information for each state.” This is how I would recommend writing a sentence to explain a table like this.