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

#### Translations

any of the three points

- Czech: kvartil

#### Derived terms

### See also

# 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:

- Use the median to divide the ordered data set into two halves. Do not include the median into the halves.
- 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

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