AskDefine | Define quartile

Dictionary Definition

quartile n : (statistics) any of three points that divide an ordered distribution into four parts each containing one quarter of the scores

User Contributed Dictionary

English

Noun

quartile (plural quartiles)
  1. Any of the three points that divide an ordered distribution into four parts, each containing a quarter of the population.
  2. Any one of the four groups so divided.
    This school is ranked in the first quartile.

Translations

any of the three points

Derived terms

Extensive Definition

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.http://www.robhyndman.info/papers/quantile.htm 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. Another possible rule would be to include the median in the halves when calculating the quartiles. This would give significantly different answers to the examples.
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 Q_1 = 15 \\ Q_2 = 40 \\ Q_3 = 43 \end
Example 2 Ordered Data Set: 7, 15, 36, 39, 40, 41
\begin Q_1 = 15 \\ Q_2 = 37.5 \\ Q_3 = 40 \end
Example 3 Ordered Data Set: 1 2 3 4
\begin Q_1 = 1.5 \\ Q_2 = 2.5 \\ Q_3 = 3.5 \end

See also

External links

quartile in Danish: Kvartil
quartile in German: Quartil
quartile in Spanish: Cuartil
quartile in Persian: چارک (آمار)
quartile in French: Quartile
quartile in Italian: Quartile
quartile in Japanese: 分位数
quartile in Dutch: Kwartiel
quartile in Polish: Kwartyl
quartile in Portuguese: Quartil
quartile in Swedish: Kvartil
quartile in Turkish: Dörttebirlik
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