# "The average is X, you can expect this to deviate to no more than Y" - what does this mean **URL:** \ **Category:** Factual Questions\ **Created:** [December 8, 2009, 12:12am UTC](https://boards.straightdope.com/t/the-average-is-x-you-can-expect-this-to-deviate-to-no-more-than-y-what-does-this-mean/520386 "2009-12-08T00:12:21Z")\ **Posts on this page:** 13\ **Page:** 1
**Author:** ![Mangetout](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/mangetout/32/19_2.png) [@Mangetout](https://boards.straightdope.com/u/Mangetout)\ **Post date:** [December 8, 2009, 12:12am UTC](https://boards.straightdope.com/t/the-average-is-x-you-can-expect-this-to-deviate-to-no-more-than-y-what-does-this-mean/520386/1 "2009-12-08T00:12:21Z")
I was googling on the subject of the average circumference of the human head and came across this Yahoo Answers post: > **[Yahoo | Mail, Weather, Search, Politics, News, Finance, Sports & Videos](https://www.yahoo.com/)** > > Latest news coverage, email, free stock quotes, live scores and video are just the beginning. Discover more every day at Yahoo! Wherein the respondent says “The average circumference of the human head is about 55.9cm for men, it is 54.47cm for women. You can expect this figure to deviate to no more than 2cm.” Does this mean something other than I straightforwardly read it to mean? (that is, 55.9 plus or minus 2, but that’s all) Or is this one of those terminology things where it doesn’t quite mean what the man on the street might think, but a statistician can understand it fully? (for the curious, the reason I was exploring this topic: my bulbous head is 60cm in circumference, and I have trouble finding a hat to fit) ---
**Author:** ![Jamaika\_a\_jamaikaiake](https://avatars.discourse-cdn.com/v4/letter/j/7993a0/32.png) [@Jamaika\_a\_jamaikaiake](https://boards.straightdope.com/u/Jamaika_a_jamaikaiake)\ **Post date:** [December 8, 2009, 12:16am UTC](https://boards.straightdope.com/t/the-average-is-x-you-can-expect-this-to-deviate-to-no-more-than-y-what-does-this-mean/520386/2 "2009-12-08T00:16:46Z")
Seriously, dude, it’s Yahoo Answers. You shouldn’t expect precise terminology or accurate information. Obviously it isn’t true that all men have heads 55.9 +/- 2 as _yours_ is outside that range. Maybe the 2cm is the standard deviation, or (and this is more likely) the person is talking out of their ass. ---
**Author:** ![Mangetout](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/mangetout/32/19_2.png) [@Mangetout](https://boards.straightdope.com/u/Mangetout)\ **Post date:** [December 8, 2009, 12:20am UTC](https://boards.straightdope.com/t/the-average-is-x-you-can-expect-this-to-deviate-to-no-more-than-y-what-does-this-mean/520386/3 "2009-12-08T00:20:22Z")
I fully understand the unreliability of Yahoo Answers - I’m not asking about the reliability of this information - just whether that phraseology has meaning that is obscure to the layman. ---
**Author:** ![Contrapuntal](https://avatars.discourse-cdn.com/v4/letter/c/e274bd/32.png) [@Contrapuntal](https://boards.straightdope.com/u/Contrapuntal)\ **Post date:** [December 8, 2009, 12:21am UTC](https://boards.straightdope.com/t/the-average-is-x-you-can-expect-this-to-deviate-to-no-more-than-y-what-does-this-mean/520386/4 "2009-12-08T00:21:56Z")
> [@Jamaika\_a\_jamaikaiake](#): > > Seriously, dude, it’s Yahoo Answers. You shouldn’t expect precise terminology or accurate information. > > Obviously it isn’t true that all men have heads 55.9 +/- 2 as _yours_ is outside that range. Maybe the 2cm is the standard deviation, or (and this is more likely) the person is talking out of their ass. Maybe **Mangetout** ’s head isn’t human. Did you ever think about that? ---
**Author:** ![Jamaika\_a\_jamaikaiake](https://avatars.discourse-cdn.com/v4/letter/j/7993a0/32.png) [@Jamaika\_a\_jamaikaiake](https://boards.straightdope.com/u/Jamaika_a_jamaikaiake)\ **Post date:** [December 8, 2009, 12:26am UTC](https://boards.straightdope.com/t/the-average-is-x-you-can-expect-this-to-deviate-to-no-more-than-y-what-does-this-mean/520386/5 "2009-12-08T00:26:00Z")
> [@Mangetout](#): > > I fully understand the unreliability of Yahoo Answers - I’m not asking about the reliability of this information - just whether that phraseology has meaning that is obscure to the layman. Fair enough. Sorry if I was condescending or anything. However, a source like Yahoo answers will also employ imprecise terminology. Thus, what the person MIGHT be referring to is [standard deviation](http://en.wikipedia.org/wiki/Standard_deviation), though I wouldn’t hold my breath. ---
**Author:** ![cerberus](https://avatars.discourse-cdn.com/v4/letter/c/71e660/32.png) [@cerberus](https://boards.straightdope.com/u/cerberus)\ **Post date:** [December 8, 2009, 12:28am UTC](https://boards.straightdope.com/t/the-average-is-x-you-can-expect-this-to-deviate-to-no-more-than-y-what-does-this-mean/520386/6 "2009-12-08T00:28:28Z")
It’s either a mangling of a confidence interval, where some knucklehead is applying the confidence level (usually 95%) to the single interval (it applies to the entire family of intervals), or the numerical estimates are being treated as the true values of a population mean and standard error of some sort. Problem - we generally do not know these true values, and normality can be suspect as an a priori assumption. While people generally lean rather heavily on the asymptotic normality of families of sample means, it is not at all clear that one can assume the normality of the underlying population. ---
**Author:** ![statsman1982](https://avatars.discourse-cdn.com/v4/letter/s/e79b87/32.png) [@statsman1982](https://boards.straightdope.com/u/statsman1982)\ **Post date:** [December 8, 2009, 12:51am UTC](https://boards.straightdope.com/t/the-average-is-x-you-can-expect-this-to-deviate-to-no-more-than-y-what-does-this-mean/520386/7 "2009-12-08T00:51:39Z")
My money is on a rather loose interpretation of standard deviation, which is an average squared deviation from the mean. The standard deviation can be interpreted as the expected deviation from the mean. But I agree, the answer was poorly phrased. ---
**Author:** ![pulykamell](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/pulykamell/32/3166_2.png) [@pulykamell](https://boards.straightdope.com/u/pulykamell)\ **Post date:** [December 8, 2009, 2:14am UTC](https://boards.straightdope.com/t/the-average-is-x-you-can-expect-this-to-deviate-to-no-more-than-y-what-does-this-mean/520386/8 "2009-12-08T02:14:05Z")
> [@statsman1982](#): > > My money is on a rather loose interpretation of standard deviation, which is an average squared deviation from the mean. [nitpick]It’s the square root of the average squared deviation from the mean. Variance is the average squared deviation from the mean. [/nitpick] ---
**Author:** ![cerberus](https://avatars.discourse-cdn.com/v4/letter/c/71e660/32.png) [@cerberus](https://boards.straightdope.com/u/cerberus)\ **Post date:** [December 8, 2009, 2:17am UTC](https://boards.straightdope.com/t/the-average-is-x-you-can-expect-this-to-deviate-to-no-more-than-y-what-does-this-mean/520386/9 "2009-12-08T02:17:07Z")
Even more nit-picky, the use of hard numbers suggests that these are sample-based estimates of means, standard deviations, yada yada, which do not support probabilistic statements about population behavior. ---
**Author:** ![don\_t\_ask](https://avatars.discourse-cdn.com/v4/letter/d/e68b1a/32.png) [@don\_t\_ask](https://boards.straightdope.com/u/don_t_ask)\ **Post date:** [December 8, 2009, 2:24am UTC](https://boards.straightdope.com/t/the-average-is-x-you-can-expect-this-to-deviate-to-no-more-than-y-what-does-this-mean/520386/10 "2009-12-08T02:24:01Z")
[Here](http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1793909/?page=2) is a better answer to Big Head’s original thought about his abnormally large cranium. Not so big it seems. ---
**Author:** ![statsman1982](https://avatars.discourse-cdn.com/v4/letter/s/e79b87/32.png) [@statsman1982](https://boards.straightdope.com/u/statsman1982)\ **Post date:** [December 8, 2009, 2:46am UTC](https://boards.straightdope.com/t/the-average-is-x-you-can-expect-this-to-deviate-to-no-more-than-y-what-does-this-mean/520386/11 "2009-12-08T02:46:55Z")
> [@pulykamell](#): > > [nitpick]It’s the square root of the average squared deviation from the mean. Variance is the average squared deviation from the mean. > [/nitpick] :smack: Not a nitpick by any stretch of the imagination, however. A nitpick would be arguing over using n vs. n-1 in the denominator of the sample estimate of the standard deviation, as both are asymptotically unbiased. The square root operator is pretty crucial to the whole calculation. I thank you for pointing out my omission. Now I will go over to the corner and flagellate myself for making such a stupid error.😛 ---
**Author:** ![statsman1982](https://avatars.discourse-cdn.com/v4/letter/s/e79b87/32.png) [@statsman1982](https://boards.straightdope.com/u/statsman1982)\ **Post date:** [December 8, 2009, 2:55am UTC](https://boards.straightdope.com/t/the-average-is-x-you-can-expect-this-to-deviate-to-no-more-than-y-what-does-this-mean/520386/12 "2009-12-08T02:55:52Z")
Actually, the sample standard deviation using the (n-1) denominator is unbiased for all n. ---
**Author:** ![cerberus](https://avatars.discourse-cdn.com/v4/letter/c/71e660/32.png) [@cerberus](https://boards.straightdope.com/u/cerberus)\ **Post date:** [December 8, 2009, 3:10am UTC](https://boards.straightdope.com/t/the-average-is-x-you-can-expect-this-to-deviate-to-no-more-than-y-what-does-this-mean/520386/13 "2009-12-08T03:10:05Z")
From the linked article: > [@](#): > > Abstract > > Reference range for head circumference on the Tanner charts do not go beyond age 16. In this study the head circumference and heights of 354 adults in two British centres were measured. The centile charts constructed from these measurements show that adult head circumference is related to height. The mean head circumference of a male of average height is above the 97th centile for a 16 year old on the Tanner charts. The paediatric charts are therefore inappropriate for use in adult males. These things rely on samples - the answers in play are hopelessly sloppy in terms of population versus sample. The wording of the “best” answer refers to the population mean, or it seems to, since the word “sample” does not appear. I do like the distinction between adult male and male child populations, though.