Talk:Standard deviation

Restoring technical calculator resource

I noticed the External Links section was recently removed. I am the editor who updated the LaTeX notation in the 'Rapid calculation methods' section earlier today to improve the article's technical clarity. Regarding the external link I provided (Firgelli), it is a live, high-precision tool that supports Bessel's correction and weighted calculations—both core themes of this article.

I replaced the previous link (standard-deviation-calculator.net) because it was a low-utility site. If an 'External Links' section is to be maintained, I believe it should point to tools that handle the advanced cases discussed in the text, such as step-by-step variance derivations. I'd appreciate feedback on whether this resource meets the community's standards for utility. ProjectAutomate (talk) 20:38, 27 March 2026 (UTC)

Wikipedia isn't for supplying calculators. Sure, if there is one out there with many citations and/or is otherwise notable and reliable, we sometimes would include it. The calculator you are adding was posted March 8, 2026 according to itself. That alone would seem to indicate that it is not reliable as a source. I could be wrong, but if were forced to make a guess with no additional information, I would guess that this case is instead more like low-level WP:CITESPAM. —Quantling (talk | contribs) 21:21, 27 March 2026 (UTC)

Fair point, Quantling. I saw the External Links section was a bit of a mess with that old .net site and thought a high-precision tool would be a better fit, but I'll defer to the community standards on that. My primary interest is just cleaning up the LaTeX notation and technical clarity in these articles. Thanks for the heads-up on the policy. ProjectAutomate (talk) 21:33, 27 March 2026 (UTC)

Expected value

It was not good before, but there was a link to expected value (from the word average, which was not ideal). Is that link still needed somewhere? Jens Ahlström (talk) 01:49, 30 March 2026 (UTC)

Examples for "Unbiased sample standard deviation" factor wrong

I am pretty sure that the biases given for n=3 and n=9 are wrong. Using the given formula I get in R

> for (n in c(3,9))

print(c(n,1/((sqrt(2/(n-1))*gamma(n/2)/gamma((n-1)/2)))))

[1] 3.000000 1.128379

[1] 9.000000 1.031661

which corresponds to 13% (not 1.3%) and 3% (not smaller than 0.1%). That these values are correct can be seen by:

> s=c(); for (i in 1:10000) s=c(s,sd(rnorm(3)))

> 1/mean(s)

[1] 1.128619 ~2026-41396-52 (talk) 13:28, 24 July 2026 (UTC)

I have corrected them. DSNice (talk) 13:51, 24 July 2026 (UTC)

95% within 2 standard deviations

In the second paragraph: "...approximately 68% of all values fall within one standard deviation of the average, 95% within two standard deviations, and 99.7% within three".

To me, this is a bit confusing if I didn't know that 95% of all values fall within 1.96 standard deviations, NOT 2. The round numbers make it seem like 95% falls exactly within 2 standard deviations. Should this be changed?

Perhaps it should say something like "...approximately 68% of all values fall within one standard deviation of the average, 95% within roughly two standard deviations, and 99.7% within three". Or something to that effect? Chippea (talk) 11:44, 26 August 2026 (UTC)

I think the original intent of whoever wrote the sentence was the the "approximately" used before 68% also applies to 95%. I agree that the current phrasing is not idea, because it is a bit ambiguous. One possible solution would be:

approximately 68% of all values fall within one standard deviation of the average; approximately 95% within two standard deviations; and approximately 99.7% within three.

But that's a bit heavy, and also unnecessary since all these numbers are "obviously" approximations anyway. Another solution would be to improve the estimate:

approximately 68.3% of all values fall within one standard deviation of the average, 95.4% within two standard deviations, and 99.7% within three.

This makes it easier to remember that all those numbers are approximations. Malparti (talk) 12:05, 26 August 2026 (UTC)

After having a closer look at the style pages, I think your second suggestion would be best in this case as it maintains precision for all three numbers. Chippea (talk) 21:34, 26 August 2026 (UTC)

I have edited the article to be in line with your second suggestion. Thanks for the help. Chippea (talk) 00:12, 27 August 2026 (UTC)

I think the existing article text is okay. The "approximately" for one standard deviation is implied for the other cases. Although slightly less good IMHO, I won't protest if we add an explicit "approximately" to the latter two cases (to describe their percentages, not their count of standard deviations). If that's too wordy ... the tilde symbol could be used: approximately 68% of all values fall within one standard deviation of the average; ~95% within two standard deviations; and ~99.7% within three. —Quantling (talk | contribs) 17:45, 26 August 2026 (UTC)