OpenLLM-France/wikimedia huggingface dataset:
# Handbook of Descriptive Statistics/Measures of Central Tendency/Arithmetic Mean
## Description

Most commonly used measure of central tendency.
    ${\overline {x}}={\frac {1}{n}}\sum _{i=1}^{n}x_{i}$
Wikipedia article: Arithmetic mean

## Usages

* The mean may be conceived of as an estimate of the median. When the mean is not an accurate estimate of the median, the set of numbers, or frequency distribution, is said to be skewed.
* The arithmetic mean is greatly influenced by outliers. For instance, reporting the "average" annual income in Redmond, Washington as the arithmetic mean of all annual incomes would yield a surprisingly high number because of Bill Gates. These distortions occur when the mean is different from the median, and the median is a superior alternative when that happens.
* In certain situations, the arithmetic mean is the wrong concept of "average" altogether. For example, if a stock rose 10% in the first year, 30% in the second year and fell 10% in the third year, then it would be incorrect to report its "average" increase per year over this three year period as the arithmetic mean (10% + 30% + (−10%))/3 = 10%; the correct average in this case is the geometric mean which yields an average increase per year of only 8.8%.

## Distributions

* Include standard values for common distributions, if they exist. For example, a normal distribution always has a skew and kurtosis of zero.
* Include standard error for normal distribution, and for other distributions also if possible.
For a normal distribution, the standard error of the mean is:
    σ$_M$ = σ / sqrt(N)
* Sampling distribution.

## Calculation

Include any alternative methods of calculation, especially for large data sets, or when other measures have already been calculated.

## Software
### Microsoft Excel

It is relatively easy to determine the arithmetic mean, or average, in Microsoft Excel (v. '97, 2000, 2002/XP) by using a simple equation. Follow these steps to determine the mean in Excel for a set of data:
* Highlight an empty cell in the worksheet in which the mean will be calculated.
* Assuming that there are ten data points in cells A1 through A10, the following equation could be typed in the empty cell: "=AVERAGE(A1:A10)". Alternatively, this equation can also accept arguments in the form: "=AVERAGE(A1,A2,A3,...,A10)"
Refer to Microsoft Excels application documentation for further help.

### Minitab

In Minitab (v. 14), finding the arithmetic mean is as simple as choosing options from the menu to display several descriptive statistics at once, including the arithmetic mean. Assuming again that there are ten valid data points in column C1, follow the steps below to display the mean:
* Go to the Menu bar at the top of the Minitab application and choose the following options: Stat -> Basic Statistics -> Display Descriptive Statistics...
* In the box labeled "Variables:" on the right hand side of the dialog box that appears, type "C1" and then click on the "OK" button in the bottom center of the dialog box. The mean will then be displayed in addition to other useful statistics in the 'Session' window of Minitab.
# Handbook of Descriptive Statistics/Measures of Central Tendency/Mode

Modes are the most common values in a data set.
Example: Of the data set
1, 2, 3, 4, 4, 4, 5, 6
4 is the mode because there are three responses of "4" and only one response for 1, 2, 3, 5, or 6.
Data can have more than one mode, example:
Of the data set
1, 2, 2, 3, 4, 5, 5, 6.
2 and 5 are the modes because they are equally the most frequent.
Histograms can often be a good way to see if large data sets have more than one mode.
# Handbook of Descriptive Statistics

This book aims to function as a comprehensive reference guide to the measures used in descriptive statistics. For a general introduction to statistics, see Statistics instead.
It has a section on all the common measures, and they are categorised according to type. Initially we shall concentrate on univariate statistics. Entries should be brief, information-packed and not overly tutorial in nature. Assume a reader which already has a basic knowledge of statistics, and needs detailed information or a refresher.
See Template for how an entry should look.

## Table of contents

* Introduction
* Types of Statistical Variables
* Measures of Central Tendency
** Arithmetic Mean
** Median
** Mode
** Midrange
** Geometric Mean
** Harmonic Mean
** Truncated Mean
** Interquartile Mean
** Root Mean Square
** Trimean
* Measures of Statistical Variability
** Variance
** Population Variance
** Standard Deviation
** Range
** Interquartile range
** Semiquartile range
** Absolute Deviation
** Geometric Standard Deviation
* Measures of Distribution Shape
** Skewness
** Kurtosis
** Chi-Squared Goodness of Fit
** Shapiro-Wilks W
** Kolmogorov-Smirnov test
# Handbook of Descriptive Statistics/Measures of Central Tendency/Geometric Mean

The geometric mean of a set of N numbers is the Nth root of their product.
An alternate method for calculation of the geometric mean is to first calculate its logarithm, which is the arithmetic mean of the logs of the original numbers.
# Handbook of Descriptive Statistics/Measures of Central Tendency/Harmonic Mean

Harmonic mean is most commonly preferred when the data is given in terms of speed (e.g. km/hour), rate (e.g. kg/rupee) etc. The harmonic mean is defined as the reciprocal of arithmetic mean of reciprocals of the items in a given series.
# Handbook of Descriptive Statistics/Measures of Central Tendency/Midrange

The midrange is defined as the average of the high and the low observations in a dataset. Because it is a linear combination of order statistics, it falls in the class of L-estimates.
Although it uses order statistics in its calculation, the statistic can be influenced by a single bad observation on the high or low side.
# Handbook of Descriptive Statistics/Measures of Central Tendency/Trimean

The trimean is a resistant measure of central tendency.
Instead of focusing on the median, the trimean is calculated by adding twice the sum of the median to the sum of the 25th percentile and 75th percentile and then divide the sum by four.
(25%ile + 2* 50%ile + 75%ile) / 4 = Trimean
John Tukey came up with this in a 1982 publication. This is part of the family of L-Estimates which are statistics based on linear combination of the order statistics.
Because it depends on order statistics it is a robust measure, but by including the 25%ile and 75%ile this lowers the breakdown value of the measure.
# Handbook of Descriptive Statistics/Measures of Distribution Shape/Skewness

A normal curve is bilaterally symmetrical. Skewness is a measure of departure from a normal curve. The coefficient of skewness is a statistical measure of asymmetry of a curve. The coefficient of skewness in a normal curve is zero.
# HyperText Markup Language/Tag List/bdo
## Use

This reverses the text that is embedded in it. Used when dealing with other languages that write from right to left. For example Arabic.

## Example

This will return the text backwards. e.g. (.sdrawkcab eb lliw txet sihT)

## Required attributes
#### dir

Either choose "ltr" for left to right or "rtl" for right to left. This declares what direction the text goes.

## More info

A link to a page with more info, then the name of the site the info came from (i.e. W3Schools).
# HyperText Markup Language/Tag List/area
## Use

For specifying coordinates of image maps.

## Required attributes
#### coords

The coordinates of area in image map.

#### href

The link to another page specified.

#### shape

Defining the shape of the image map.

## Optional attributes
#### accesskey

For adding keyboard shortcuts instead of clicking on the area.

#### alt

For giving information about the area.

#### nohref

For making a click on the area mean nothing.

#### target

For declaring the window or frame the link shall be displayed in.

## Standard attributes

* accesskey
* alt
* coords
* href
* nohef
* shape
* target

## More info

A link to a page with more info, then the name of the site the info came from (i.e. W3Schools).
# HyperText Markup Language/Tag List/applet
## Use

This is a depreciated tag. Use <object/> instead. It was used for applying Java Applets to the page. It was also used in conjunction with JavaScript.

## Required attributes
#### code

For specifying the URL of the applet code.

## Optional attributes
#### align

How the applet is to be aligned with the text and images.

#### alt

Text that will be displayed if the browser does not support the applet tag.

#### archive

The name of the .zip file containing the file.

#### codebase

The class file subdirectory.

#### height

For specifying the height of the applet.

#### hspace

The horizontal space around the applet in pixels.

#### mayscript

Allows the applet to access a JavaScript or vbscript.

#### name

The name of the applet that will be accessed via a DOM.

#### vspace

The amount of vertical space around the applet in pixels.

#### width

For specifying the width of the applet.

## Standard attributes

* code
* width
* height

## More info

A link to a page with more info, then the name of the site the info came from (i.e. W3Schools).
# HyperText Markup Language/Tag List/basefont
## Use

Used to declare the default color, face and size in the text on the webpage. This is now a deprecated tag, use CSS instead.

## Required attributes
#### color

For declaring the color of the text. Can be declare as a HEX color or by color name

#### face

To declare the font that will be used in the text.

#### size

For specifying the size of the text. Choose a number between One to Seven. Three is the default.

## Standard attributes

* color
* face
* size

## More info

A link to a page with more info, then the name of the site the info came from (i.e. W3Schools).
# HyperText Markup Language/Tag List/address
## Use

The address tag marks contact information.

## More info

See http://www.w3.org/TR/html-markup/address.html
# HyperText Markup Language/Tag List/bgsound
## Use

This lets the user link a sound to a page that will play automatically whenever a client opens the webpage.

## Required attributes
#### src

This works like the img tag. It finds the source of the music file that the user wants to be played in the background.

#### loop

This tells the browser how many times the sound will be played in the background.

## Standard attributes

* src
* loop

## More info

A link to a page with more info, then the name of the site the info came from (i.e. W3Schools).
# HyperText Markup Language/Tag List/acronym
## Use

Use when dealing with an acronym in a webpage. NOTE: Most HTML coders use the abbr tag.

## Required attributes
#### title

Use this when you want the meaning of the acronym to be displayed when the mouse hvrs over the word.

## Standard attributes

* title

## More info

A link to a page with more info, then the name of the site the info came from (i.e. W3Schools).
# HyperText Markup Language/Tag List/b
## Use

For displaying text in a bold format. No attributes.
# HyperText Markup Language/Tag List/base
## Use

This sets a default target on the page.

## Required attributes
#### target

To declare the default target for the links on the page.

## Optional attributes
#### href

To declare the URL to be used to retrieve the webpage wanted.

## Standard attributes

* target
* href

## More info

A link to a page with more info, then the name of the site the info came from (i.e. W3Schools).
# HyperText Markup Language/Tag List/abbr
## Use

Use this when you want to add a meaning to an abbreviation or acronym.

## More info

A link to a page with more info, then the name of the site the info came from (i.e. W3Schools).
# Genes, Technology and Policy
## Table of Contents

* Preface
* Introduction
* The Science
* Applications in Medicine
* Applications in Agriculture
* Ownership Of and Access to Biotechnology
* References
* Notes
* About the Author
* Contributors
* Acknowledgements

## Information

This book is donated by UNDP Asia-Pacific Development Information Programme (UNDP-APDIP) to the community. The original publication by:
Author: Jose Maria A. Ochave © UNDP-APDIP, 2003, 52 pages
is located at http://www.apdip.net/publications/iespprimers/eprimer-genes.pdf
This wikibook is available under the terms of GNU Free Documentation License and Creative Commons Attribution License 2.5

## Notes

Numbers that are just placed in the middle of the sentence are citations, and should be linked to the Notes page. Do not delete these citation numbers! Use the {{gtpcite}} template to link them instead.
# General Topology/Simplicial complexes

There are several types of simplicial complexes.
Definition (semisimplicial set):
A semisimplicial set is a contravariant functor from the category ${\mathcal {N}}$ of finite sets and monotone maps to ${\textbf {Set}}$.
Definition (Δ-complex):
A Δ-complex is a topological space $X$ together with a family of functions $\sigma _{\alpha }:\Delta _{\alpha }\to X$ such that
* for each $\alpha$, the set $\Delta _{\alpha }$ is the standard simplex of a certain dimension $n$ with the subspace topology induced by the topology of $\mathbb {R} ^{n+1}$ on it,
* for each $x\in X$ there exists a unique $\alpha$ and $z\in {\overset {\circ }{\Delta }}_{\alpha }$ (the interior) so that $x=\sigma _{\alpha }(z)$,
* the topology of $X$ coincides with the final topology with respect to the $\sigma _{\alpha }$,
* and if $\Delta _{\alpha }$ is not the trivial simplex and $n\geq 1$ is its dimension, then the map arising from mapping $\Delta _{n-1}$ to any face of $\Delta _{\alpha }$ and then applying $\sigma _{\alpha }$ equals $\sigma _{\beta }$ for some $\beta$.
# Genes, Technology and Policy/About the Author
## About the Author

Jose Maria A. Ochave is a chemical engineer and lawyer. He obtained his B.S. in Chemical Engineering and Bachelor of Laws degrees from the University of the Philippines – Diliman, and his Master of Laws degree from the University of Michigan at Ann Arbor. He is currently Assistant Vice President at United Laboratories, Inc., Professor-II at the Philippine Judicial Academy, and member and legal advisor of the National Committee on Biosafety of the Philippines. He advises various Philippine government agencies and non-governmental organizations on legal and policy issues relating to biosafety, intellectual property, biotechnology, and technology transfer.
# Genes, Technology and Policy/Acknowledgements
## Acknowledgment

The author acknowledges his debt of gratitude to the scientists who reviewed the earlier drafts: Dr. William G. Padolina, Deputy Director for Partnerships of the International Rice Research Institute, and Dr. Tantono Subagyo, Deputy for Intellectual Property Rights, Intellectual Property and Technology Transfer Office, Agency for Agricultural Research Development, Republic of Indonesia. Acknowledgments are likewise in order for Dr. Emmanuel C. Lallana and Ms. Patricia J. Pascual of Digital Philippines for their patience and understanding.
# Genes, Technology and Policy/Introduction
## Introduction

Rapid advances in information technology, particularly in the area of bioinformatics, have played a critical role in breakthrough applications of modern biotechnology in medicine and agriculture. Bioinformatics, broadly defined as the use of computers to handle biological information, has made possible the genomic era. Bioinformatics provides the computer tools and databases to search, store, analyze and compare these data and to use them to develop, among others, safe and more effective medicines as well higher – yielding, more stress – resistant crops that have the potential for accelerating human development.
However, as the Human Development Report 2001 points out, this potential cannot be realized unless the two conditions are met. First, modern biotechnology has to be utilized to address the key health and agriculture challenges facing poor countries. Second, modern biotechnology has to be utilized through a systematic approach that allows potential risks to human health, environment and social equity to be effectively assessed and managed.
This primer discusses the science and policy issues surrounding the use of modern biotechnology. It provides a snapshot of its benefits as well as concerns regarding its potential negative impact on the environment and on the human health. The primer is divided into four parts. The first part is on the science behind modern biotechnology. The second part discusses the various issues relating to the application of modern biotechnology to medicine. The third part focuses on the benefits and concerns relating to the use of modern biotechnology in agriculture. Finally, the fourth part discusses ownership and access issues viewed from the perspective of developing countries.
This primer is by no means comprehensive. It is intended merely to introduce readers to the various perspectives in the ongoing debate on the use of modern biotechnology. Readers are therefore encouraged to consult the list of references at the end of the primer.
# History of the National Hockey League/1917–1942/Rules and innovations
## Rules and innovations

The 1920s saw numerous rule innovations as the sport evolved. The Ottawa Senators won three Stanley Cups in the early 1920s using strong defence, and the goaltending of Clint Benedict, who recorded a record five shutouts in a 24-game season in 1921. The Senators employed a strategy where they kept both defencemen and a forward in their own zone at all times after they gained a lead. After the Senators' third championship in 1924, Frank Calder made it illegal for more than two players to be in their defensive zone if the puck was not.
Defence continued to dominate the game, however, as in 1928–29, the league averaged less than three goals per game. Canadiens goaltender George Hainsworth set what remains a league record with 22 shutouts in only 44 games. As a result, the league allowed the use of the forward pass in all zones beginning in 1929. Previously, forward passing was allowed only in the defensive and neutral zones. The change saw offence rise to 6.9 goals per game over the first third of the season as players began to park themselves on their opponent's goal crease. The league responded by introducing the offside rule early in the 1929–30 season, barring offensive players from entering their opponent's zone before the puck. Despite this, Cooney Weiland, Dit Clapper and Howie Morenz all broke the 40-goal mark, the first players to do so since Joe Malone scored 44 in the NHL's first season.
Boston Bruins governor, Charles Adams had long disliked the defensive tactic of shooting the puck the length of the ice ("icing") to relieve pressure. After the New York Americans iced the puck 61 times in a 3–2 win in Boston during the 1936–37 season, Adams promised that he would see to it that the Bruins played a similar style in New York. True to his word, the Bruins iced the puck 87 times in a 0–0 tie at Madison Square Garden. The NHL introduced the icing rule the following season, calling for a faceoff in the offending team's defensive zone after each infraction.
Art Ross was an early innovator of the game. He designed rounded goal nets that became the league standard, replacing the old square-backed nets. He also successfully argued for using synthetic rubber pucks rather than real rubber. Some of Ross' inventions did not catch on, however. Ross invented a puck with rounded edges that was rejected after goaltenders complained about the erratic behaviour of the pucks. He also created a two-piece hockey stick that had a metal shaft and replaceable wooden blades. The idea did not catch on at the time, but became a forerunner to modern composite sticks used today.
# History of the National Hockey League/1917–1942/Rules and innovations/Clint Benedict

Clint Benedict became the first goaltender to wear facial protection during a game, as he donned a leather mask to protect a broken nose on January 20, 1930. The mask obscured Benedict's vision, and he abandoned it shortly after. Later that season, Benedict was again hit by a puck, effectively ending his NHL career. It was not the first attempt at changing how goaltenders played their position. When the NHL was formed, the league abandoned the rule forbidding goaltenders from leaving their feet to make a save. While the NHA imposed a $2 fine every time a goalie left his feet, Calder dismissed the idea for the NHL. He was quoted as saying: "as far as I'm concerned, they can stand on their head if they choose to". The phrase became, and remains today, a popular way to describe a goaltender who plays a great game.
# History of the National Hockey League/1917–1942/Great Depression/Six-team league
### Six-team league

In financial difficulty, and unable to compete with the Canadiens for fan support in Montreal, the Maroons suspended operations prior to the 1938–39 season after being denied permission to relocate to St. Louis. Six Maroons players were transferred to the Canadiens while three were sold to the Black Hawks. The Americans, also struggling in New York and under the control of the league, were turned over to Red Dutton in 1940 with orders to improve the club's finances. By 1942, 90 players had left the NHL for active duty during World War II. Continuing to struggle financially, and due to a lack of players, the Americans were suspended prior to the 1942–43 season. Thus began what became known as the "Original Six" era of the National Hockey League.
# History of the National Hockey League/1917–1942/Toronto Maple Leafs

* Eddie Livingstone, cont.
* /Maple Leaf Gardens
* /Conn Smythe
* /Ace Bailey
* /1942 Stanley Cup Finals
# History of the National Hockey League/1917–1942/Toronto Maple Leafs/1942 Stanley Cup Finals

In the 1942 Stanley Cup Finals, the heavily favoured Maple Leafs initially found themselves unable to counter the fifth-place Red Wings' strategy of firing the puck into the offensive zone then chasing after it, losing the first three games of the final as a result. Jack Adams' "dump-and-chase" tactic led Leafs goaltender Turk Broda to declare the Wings "unbeatable". Toronto rebounded, however, winning the final four games, and the Stanley Cup. The 1942 Leafs remain the only team in NHL history to come back from a 3–0 deficit to win a championship series.
# History of the National Hockey League/1917–1942/Great Depression/Howie Morenz
### Howie Morenz

At the same time as other teams folded, the league reduced its salary cap to $62,500 per team, and $7,000 per player. Several well-paid star players were traded as teams attempted to fit under the cap. The biggest name was Montreal's Howie Morenz, a three-time Hart Trophy winner, two-time scoring leader and the face of the Canadiens organization. Drawing only 2,000 fans per game in an arena that held 10,000, Canadiens owner Leo Dandurand sent his star to the Black Hawks. The Montreal fans voiced their opinion of the deal by giving Morenz a standing ovation when he scored against the Canadiens on the last day of the 1935 season. Less than two seasons later, Morenz was traded back to Montreal after a brief time playing for the Rangers.
On January 28, 1937, Morenz's skate caught on the ice while he was being checked by Chicago's Earl Seibert, suffering a broken leg in four places. On March 8, Morenz died of a coronary embolism. Morenz's teammate, Aurel Joliat, had a different explanation of his death: "Howie loved to play hockey more than anyone ever loved anything, and when he realized that he would never play again, he couldn't live with it. I think Howie died of a broken heart." On the day of his funeral, 50,000 people filed past Morenz's casket at centre ice of the Montreal Forum to pay their last respects to the man the media called "the Babe Ruth of hockey". A benefit game held in November 1937 raised $20,000 for Morenz's family as the NHL All-Stars defeated the Montreal Canadiens 6–5. Morenz was one of the first players elected to the Hockey Hall of Fame when it was created in 1945.