Quartile

Quartile

A quartile is a type of quantile which divides the number of data points into four more or less equal parts, or quarters. The data must be ordered from smallest to largest to compute quartiles.

Definition

The first quartile (Q1) is defined as the middle number between the smallest number and the median of the data set. The second quartile (Q2) is the median of the data. The third quartile (Q3) is the middle value between the median and the highest value of the data set.

Calculation

There are several methods for calculating quartiles. One common method, called the Tukey method, involves finding the median of the data set, then finding the medians of the two halves of the data set. The first quartile is the median of the lower half of the data, not including the median if the data set has an odd number of observations. The third quartile is the median of the upper half of the data.

Use

Quartiles are used in statistics and other mathematical disciplines to provide a robust measure of scale and to detect and handle outliers. They are also used in box plots, probability theory, and sampling.

See also

• Percentile
• Interquartile range
• Median
• Box plot
• Descriptive statistics

References

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External links

• Quartiles on Maths Is Fun
• Khan Academy: Box plot review

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