Typing non-Unicode statistics characters
04-24-2022, 12:03 AM
Post: #1
 Joe Horn Senior Member Posts: 1,859 Joined: Dec 2013
Typing non-Unicode statistics characters
Many HP calculators use $$\bar{x}$$ ("x-bar") and $$\hat{y}$$ ("y-hat") as statistics functions, but these characters do not exist in Unicode, and would therefore seem impossible to type in this forum. However, they are easy to make using TEX, like this:

$$\bar{x}$$ is typed as $$\bar{x}$$
$$\hat{y}$$ is typed as $$\hat{y}$$

"Widehat" sometimes creates a slightly more visible caret than "hat".

<0|ɸ|0>
-Joe-
04-24-2022, 12:40 PM
Post: #2
 Thomas Klemm Senior Member Posts: 1,711 Joined: Dec 2013
RE: Typing non-Unicode statistics characters
(04-24-2022 12:03 AM)Joe Horn Wrote:  but these characters do not exist in Unicode

You can use Combining Diacritical Marks:

x̄ ȳ z̄
x̂ ŷ ẑ

This works also in code blocks:
Code:
x̄ ȳ z̄ x̂ ŷ ẑ $$\bar{x}$$ $$\hat{y}$$

You can copy them from here and paste them following the character.

U+0302: COMBINING CIRCUMFLEX ACCENT
U+0304: COMBINING MACRON

However, the result seems to depend on the chosen font (here: Impact):

x̄ ȳ z̄
x̂ ŷ ẑ
04-24-2022, 12:56 PM
Post: #3
 Thomas Okken Senior Member Posts: 1,777 Joined: Feb 2014
RE: Typing non-Unicode statistics characters
In Safari on my iPhone, the ^ in Joe's post end up to the right of the y.
The ones in Thomas' post look OK.
04-24-2022, 01:37 PM (This post was last modified: 04-24-2022 01:39 PM by Joe Horn.)
Post: #4
 Joe Horn Senior Member Posts: 1,859 Joined: Dec 2013
RE: Typing non-Unicode statistics characters
(04-24-2022 12:56 PM)Thomas Okken Wrote:  In Safari on my iPhone, the ^ in Joe's post end up to the right of the y.
The ones in Thomas' post look OK.

Interesting! Conversely, Thomas Klemm's method sometimes fails in Edge on my laptop. The following is from a screen capture of his posting:

Please ignore the following TEX experiment, which I'll check on various browsers & platforms.

$$\bar{x}$$ $$\bar{y}$$ $$\bar{z}$$
$$\widehat{x}$$ $$\widehat{y}$$ $$\widehat{z}$$

<0|ɸ|0>
-Joe-
04-24-2022, 02:59 PM
Post: #5
 Massimo Gnerucci Senior Member Posts: 2,474 Joined: Dec 2013
RE: Typing non-Unicode statistics characters
(04-24-2022 12:40 PM)Thomas Klemm Wrote:  U+0304: COMBINING MACRON

**Warning**
Election day in France!

:)

Greetings,
Massimo

-+×÷ ↔ left is right and right is wrong
04-24-2022, 05:18 PM
Post: #6
 Thomas Klemm Senior Member Posts: 1,711 Joined: Dec 2013
RE: Typing non-Unicode statistics characters
LaTeX

bar
$$\bar{a} \bar{b} \bar{c} \bar{d} \bar{e} \bar{f} \bar{g} \bar{h} \bar{i} \bar{j} \bar{k} \bar{l} \bar{m} \bar{n} \bar{o} \bar{p} \bar{q} \bar{r} \bar{s} \bar{t} \bar{u} \bar{v} \bar{w} \bar{x} \bar{y} \bar{z}$$

overline
$$\overline{a} \overline{b} \overline{c} \overline{d} \overline{e} \overline{f} \overline{g} \overline{h} \overline{i} \overline{j} \overline{k} \overline{l} \overline{m} \overline{n} \overline{o} \overline{p} \overline{q} \overline{r} \overline{s} \overline{t} \overline{u} \overline{v} \overline{w} \overline{x} \overline{y} \overline{z}$$

hat
$$\hat{a} \hat{b} \hat{c} \hat{d} \hat{e} \hat{f} \hat{g} \hat{h} \hat{i} \hat{j} \hat{k} \hat{l} \hat{m} \hat{n} \hat{o} \hat{p} \hat{q} \hat{r} \hat{s} \hat{t} \hat{u} \hat{v} \hat{w} \hat{x} \hat{y} \hat{z}$$

widehat
$$\widehat{a} \widehat{b} \widehat{c} \widehat{d} \widehat{e} \widehat{f} \widehat{g} \widehat{h} \widehat{i} \widehat{j} \widehat{k} \widehat{l} \widehat{m} \widehat{n} \widehat{o} \widehat{p} \widehat{q} \widehat{r} \widehat{s} \widehat{t} \widehat{u} \widehat{v} \widehat{w} \widehat{x} \widehat{y} \widehat{z}$$

This is what happens if the rendered text is copied and pasted:
Code:
bar: a¯b¯c¯d¯e¯f¯g¯h¯i¯j¯k¯l¯m¯n¯o¯p¯q¯r¯s¯t¯u¯v¯w¯x¯y¯z¯ overline: a⎯⎯⎯b⎯⎯⎯c⎯⎯⎯d⎯⎯⎯e⎯⎯⎯f⎯⎯⎯g⎯⎯⎯h⎯⎯⎯i⎯⎯j⎯⎯k⎯⎯⎯l⎯⎯m⎯⎯⎯⎯n⎯⎯⎯o⎯⎯⎯p⎯⎯⎯q⎯⎯⎯r⎯⎯⎯s⎯⎯t⎯⎯u⎯⎯⎯​v⎯⎯⎯w⎯⎯⎯⎯x⎯⎯⎯y⎯⎯⎯z⎯⎯ hat: â b̂ ĉ d̂ ê f̂ ĝ ĥ î ĵ k̂ l̂ m̂ n̂ ô p̂ q̂ r̂ ŝ t̂ û v̂ ŵ x̂ ŷ ẑ  widehat: aˆbˆcˆdˆeˆfˆgˆhˆiˆjˆkˆlˆmˆnˆoˆpˆqˆrˆsˆtˆuˆvˆwˆxˆyˆzˆ

In Math Settings -> Math Renderer of MathJax HTML-CSS is selected.

Unicode

The first line is ASCII, the following lines use Combining Diacritical Marks:
• U+0302 Circumflex Accent
• U+0304 Macron
• U+0305 Overline
In addition to that latin letters with circumflex or macron are listed.

Default

a b c d e f g h i j k l m n o p q r s t u v w x y z
â b̂ ĉ d̂ ê f̂ ĝ ĥ î ĵ k̂ l̂ m̂ n̂ ô p̂ q̂ r̂ ŝ t̂ û v̂ ŵ x̂ ŷ ẑ
ā b̄ c̄ d̄ ē f̄ ḡ h̄ ī j̄ k̄ l̄ m̄ n̄ ō p̄ q̄ r̄ s̄ t̄ ū v̄ w̄ x̄ ȳ z̄
a̅ b̅ c̅ d̅ e̅ f̅ g̅ h̅ i̅ j̅ k̅ l̅ m̅ n̅ o̅ p̅ q̅ r̅ s̅ t̅ u̅ v̅ w̅ x̅ y̅ z̅

â ê î ô û ĉ ĝ ĥ ĵ ŝ ŵ ŷ
ā ē ī ō ū

Arial

a b c d e f g h i j k l m n o p q r s t u v w x y z
â b̂ ĉ d̂ ê f̂ ĝ ĥ î ĵ k̂ l̂ m̂ n̂ ô p̂ q̂ r̂ ŝ t̂ û v̂ ŵ x̂ ŷ ẑ
ā b̄ c̄ d̄ ē f̄ ḡ h̄ ī j̄ k̄ l̄ m̄ n̄ ō p̄ q̄ r̄ s̄ t̄ ū v̄ w̄ x̄ ȳ z̄
a̅ b̅ c̅ d̅ e̅ f̅ g̅ h̅ i̅ j̅ k̅ l̅ m̅ n̅ o̅ p̅ q̅ r̅ s̅ t̅ u̅ v̅ w̅ x̅ y̅ z̅

â ê î ô û ĉ ĝ ĥ ĵ ŝ ŵ ŷ
ā ē ī ō ū

Courier

a b c d e f g h i j k l m n o p q r s t u v w x y z
â b̂ ĉ d̂ ê f̂ ĝ ĥ î ĵ k̂ l̂ m̂ n̂ ô p̂ q̂ r̂ ŝ t̂ û v̂ ŵ x̂ ŷ ẑ
ā b̄ c̄ d̄ ē f̄ ḡ h̄ ī j̄ k̄ l̄ m̄ n̄ ō p̄ q̄ r̄ s̄ t̄ ū v̄ w̄ x̄ ȳ z̄
a̅ b̅ c̅ d̅ e̅ f̅ g̅ h̅ i̅ j̅ k̅ l̅ m̅ n̅ o̅ p̅ q̅ r̅ s̅ t̅ u̅ v̅ w̅ x̅ y̅ z̅

â ê î ô û ĉ ĝ ĥ ĵ ŝ ŵ ŷ
ā ē ī ō ū

Impact

a b c d e f g h i j k l m n o p q r s t u v w x y z
â b̂ ĉ d̂ ê f̂ ĝ ĥ î ĵ k̂ l̂ m̂ n̂ ô p̂ q̂ r̂ ŝ t̂ û v̂ ŵ x̂ ŷ ẑ
ā b̄ c̄ d̄ ē f̄ ḡ h̄ ī j̄ k̄ l̄ m̄ n̄ ō p̄ q̄ r̄ s̄ t̄ ū v̄ w̄ x̄ ȳ z̄
a̅ b̅ c̅ d̅ e̅ f̅ g̅ h̅ i̅ j̅ k̅ l̅ m̅ n̅ o̅ p̅ q̅ r̅ s̅ t̅ u̅ v̅ w̅ x̅ y̅ z̅

â ê î ô û ĉ ĝ ĥ ĵ ŝ ŵ ŷ
ā ē ī ō ū

Tahoma

a b c d e f g h i j k l m n o p q r s t u v w x y z
â b̂ ĉ d̂ ê f̂ ĝ ĥ î ĵ k̂ l̂ m̂ n̂ ô p̂ q̂ r̂ ŝ t̂ û v̂ ŵ x̂ ŷ ẑ
ā b̄ c̄ d̄ ē f̄ ḡ h̄ ī j̄ k̄ l̄ m̄ n̄ ō p̄ q̄ r̄ s̄ t̄ ū v̄ w̄ x̄ ȳ z̄
a̅ b̅ c̅ d̅ e̅ f̅ g̅ h̅ i̅ j̅ k̅ l̅ m̅ n̅ o̅ p̅ q̅ r̅ s̅ t̅ u̅ v̅ w̅ x̅ y̅ z̅

â ê î ô û ĉ ĝ ĥ ĵ ŝ ŵ ŷ
ā ē ī ō ū

Times New Roman

a b c d e f g h i j k l m n o p q r s t u v w x y z
â b̂ ĉ d̂ ê f̂ ĝ ĥ î ĵ k̂ l̂ m̂ n̂ ô p̂ q̂ r̂ ŝ t̂ û v̂ ŵ x̂ ŷ ẑ
ā b̄ c̄ d̄ ē f̄ ḡ h̄ ī j̄ k̄ l̄ m̄ n̄ ō p̄ q̄ r̄ s̄ t̄ ū v̄ w̄ x̄ ȳ z̄
a̅ b̅ c̅ d̅ e̅ f̅ g̅ h̅ i̅ j̅ k̅ l̅ m̅ n̅ o̅ p̅ q̅ r̅ s̅ t̅ u̅ v̅ w̅ x̅ y̅ z̅

â ê î ô û ĉ ĝ ĥ ĵ ŝ ŵ ŷ
ā ē ī ō ū

Trebuchet MS

a b c d e f g h i j k l m n o p q r s t u v w x y z
â b̂ ĉ d̂ ê f̂ ĝ ĥ î ĵ k̂ l̂ m̂ n̂ ô p̂ q̂ r̂ ŝ t̂ û v̂ ŵ x̂ ŷ ẑ
ā b̄ c̄ d̄ ē f̄ ḡ h̄ ī j̄ k̄ l̄ m̄ n̄ ō p̄ q̄ r̄ s̄ t̄ ū v̄ w̄ x̄ ȳ z̄
a̅ b̅ c̅ d̅ e̅ f̅ g̅ h̅ i̅ j̅ k̅ l̅ m̅ n̅ o̅ p̅ q̅ r̅ s̅ t̅ u̅ v̅ w̅ x̅ y̅ z̅

â ê î ô û ĉ ĝ ĥ ĵ ŝ ŵ ŷ
ā ē ī ō ū

Verdana

a b c d e f g h i j k l m n o p q r s t u v w x y z
â b̂ ĉ d̂ ê f̂ ĝ ĥ î ĵ k̂ l̂ m̂ n̂ ô p̂ q̂ r̂ ŝ t̂ û v̂ ŵ x̂ ŷ ẑ
ā b̄ c̄ d̄ ē f̄ ḡ h̄ ī j̄ k̄ l̄ m̄ n̄ ō p̄ q̄ r̄ s̄ t̄ ū v̄ w̄ x̄ ȳ z̄
a̅ b̅ c̅ d̅ e̅ f̅ g̅ h̅ i̅ j̅ k̅ l̅ m̅ n̅ o̅ p̅ q̅ r̅ s̅ t̅ u̅ v̅ w̅ x̅ y̅ z̅

â ê î ô û ĉ ĝ ĥ ĵ ŝ ŵ ŷ
ā ē ī ō ū

Code:
a b c d e f g h i j k l m n o p q r s t u v w x y z â b̂ ĉ d̂ ê f̂ ĝ ĥ î ĵ k̂ l̂ m̂ n̂ ô p̂ q̂ r̂ ŝ t̂ û v̂ ŵ x̂ ŷ ẑ  ā b̄ c̄ d̄ ē f̄ ḡ h̄ ī j̄ k̄ l̄ m̄ n̄ ō p̄ q̄ r̄ s̄ t̄ ū v̄ w̄ x̄ ȳ z̄  a̅ b̅ c̅ d̅ e̅ f̅ g̅ h̅ i̅ j̅ k̅ l̅ m̅ n̅ o̅ p̅ q̅ r̅ s̅ t̅ u̅ v̅ w̅ x̅ y̅ z̅  â ê î ô û ĉ ĝ ĥ ĵ ŝ ŵ ŷ ā ē ī ō ū

Conclusion

LaTeX

All four variants are rendered properly.
Individual hatted letters can be copied while U+0302 is used as combining diacritic.
Therefore they are rendered correctly in the code block.

Unicode

Only the following fonts appear to support combining diacritics:
• Arial
• Courier
• Tahoma
• Times New Roman
• Code
In the other cases, another font that is as close as possible is used instead.
It appears to be Arial in case of the Default font.
However, this may be completely different on your system.

Mildly interesting is how the points of i and j are rendered differently depending on the font.
04-24-2022, 07:07 PM (This post was last modified: 04-24-2022 07:07 PM by Thomas Okken.)
Post: #7
 Thomas Okken Senior Member Posts: 1,777 Joined: Feb 2014
RE: Typing non-Unicode statistics characters
With the LaTeX code, hat placement in Safari is strange, getting the height right but the X position wrong:

This is the same in Safari on iOS and macOS.

Everything else looks OK. It even renders all the fonts with the diacritics. So Unicode support looks good.
04-24-2022, 07:22 PM
Post: #8
 Thomas Klemm Senior Member Posts: 1,711 Joined: Dec 2013
RE: Typing non-Unicode statistics characters
(04-24-2022 07:07 PM)Thomas Okken Wrote:  With the LaTeX code, hat placement in Safari is strange, getting the height right but the X position wrong…

You may use SVG instead of HTML-CSS as Math Renderer.
To switch just right-click on the rendered formula.
04-24-2022, 07:44 PM
Post: #9
 Thomas Okken Senior Member Posts: 1,777 Joined: Feb 2014
RE: Typing non-Unicode statistics characters
Yep, that works!
I only tried it in MacOS, though. I don't know how to reach that setting on the phone.
05-29-2022, 07:18 PM
Post: #10
 jte Member Posts: 165 Joined: Feb 2014
RE: Typing non-Unicode statistics characters
(04-24-2022 07:22 PM)Thomas Klemm Wrote:
(04-24-2022 07:07 PM)Thomas Okken Wrote:  With the LaTeX code, hat placement in Safari is strange, getting the height right but the X position wrong…

You may use SVG instead of HTML-CSS as Math Renderer.
To switch just right-click on the rendered formula.

I also met with success with the “Common HTML” math renderer, as shown with the following screenshot:

I thought I’d try this sort of test on the Prime bug tracking site I put together. There, I get hat placement as expected with both “HTML-CSS” and “Common HTML” rendering, as shown with the following screenshot (for “HTML-CSS”):

Different versions of MathJax are involved, namely v2.7.1 (here, when writing this) and v2.7.9 (at the the bug tracking site, when writing this); different font choices are also mentioned in the panel brought up via “About MathJax” (web TeX fonts, here; local STIX fonts, there). Looking at the HTML being produced reveals significant differences.
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