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quartile

  (kwôr'tīl', -tĭl) pronunciation
n.

The value of the boundary at the 25th, 50th, or 75th percentiles of a frequency distribution divided into four parts, each containing a quarter of the population.

[Middle English, 90 degrees apart (of the relative position of two celestial bodies), from Old French quartil, from Medieval Latin quārtīlis, of a quartile, from Latin quārtus, fourth. See quart.]


 
 

A statistical term describing a division of observations into four defined intervals based upon the values of the data and how they compare to the entire set of observations.

Investopedia Says:
Each quartile contains 25% of the total observations. Generally, the data is ordered from smallest to largest with those observations falling below 25% of all the data analyzed allocated within the 1st quartile, observations falling between 25.1% and 50% and allocated in the 2nd quartile, then the observations falling between 51% and 75% allocated in the 3rd quartile, and finally the remaining observations allocated in the 4th quartile.

Try not to confuse a quarter with a quartile.


 

Statistical measurement. The first quartile of a list is the number that has three quarters of the numbers in the list below it; the fourth quartile is the number that has three quarters of the numbers above it; the second quartile is the same as the median.

 

statistics A form of quantile; divides the range into quarters.

 

One of the values establishing the division of a series of variables into fourths, or the range of items included in such a segment.

 
Wikipedia: quartile

In descriptive statistics, a quartile is any of the three values which divide the sorted data set into four equal parts, so that each part represents 1/4th of the sampled population.

Thus:

  • first quartile (designated Q1) = lower quartile = cuts off lowest 25% of data = 25th percentile
  • second quartile (designated Q2) = median = cuts data set in half = 50th percentile
  • third quartile (designated Q3) = upper quartile = cuts off highest 25% of data, or lowest 75% = 75th percentile

The difference between the upper and lower quartiles is called the interquartile range.

There is no universal agreement on choosing the quartile values.[1] One possible rule (employed by the TI-83 calculator boxplot and 1-Var Stats functions) is as follows:

  1. Use the median to divide the ordered data set into two halves. Do not include the median into the halves.
  2. The lower quartile value is the median of the lower half of the data. The upper quartile value is the median of the upper half of the data.

The examples below assume this rule.

Example 1
Data Set: 6, 47, 49, 15, 42, 41, 7, 39, 43, 40, 36
Ordered Data Set: 6, 7, 15, 36, 39, 40, 41, 42, 43, 47, 49

\begin{cases} Q_1  = 25.5 \\ Q_2  = 40 \\ Q_3 = 42.5 \end{cases}

Example 2
Ordered Data Set: 7, 15, 36, 39, 40, 41

\begin{cases} Q_1 = 20.25 \\ Q_2 = 37.5 \\ Q_3 = 39.75 \end{cases}

Example 3
Ordered Data Set: 1 2 3 4

\begin{cases} Q_1  = 1.75 \\ Q_2  = 2.5 \\ Q_3 = 3.25 \end{cases}

See also

External links


 
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Did you mean: quartile, quartiles

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Copyrights:

Dictionary. The American Heritage® Dictionary of the English Language, Fourth Edition Copyright © 2007, 2000 by Houghton Mifflin Company. Updated in 2007. Published by Houghton Mifflin Company. All rights reserved.  Read more
Investment Dictionary. Copyright ©2000, Investopedia.com - Owned and Operated by Investopedia Inc. All rights reserved.  Read more
Business Dictionary. Dictionary of Business Terms. Copyright © 2000 by Barron's Educational Series, Inc. All rights reserved.  Read more
Measures and Units. A Dictionary of Weights, Measures, and Units. Copyright © Donald Fenna 2002, 2004. All rights reserved.  Read more
Veterinary Dictionary. Saunders Comprehensive Veterinary Dictionary 3 Edition. Copyright © 2007 by D.C. Blood, V.P. Studdert and C.C. Gay, Elsevier. All rights reserved.  Read more
Wikipedia. This article is licensed under the GNU Free Documentation License. It uses material from the Wikipedia article "Quartile" Read more

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