Statistics · BEGINNER LESSON
Quartile
A quartile is a value from an ordered data set that splits the data into four parts. Q1, Q2, and Q3 mark the 25th, 50th, and 75th percentiles, respectively.
What quartiles are
Quartiles are numbers found after sorting data from smallest to largest. They divide an ordered data set into four parts. The first quartile (Q1) is the 25th percentile, the second quartile (Q2) is the median or 50th percentile, and the third quartile (Q3) is the 75th percentile. In plain terms, about one-fourth of the data are at or below Q1, about one-half are at or below Q2, and about three-fourths are at or below Q3. [source 1]
How quartiles are used
Quartiles help describe the center and spread of data. The interquartile range, or IQR, is Q3 minus Q1 and shows the spread of the middle 50% of the data. Box plots use Q1, Q2, Q3, and the IQR to summarize a sample. In that display, the box stretches from Q1 to Q3, and the line inside marks the median. [source 0, source 1]
[1] nature methods | VOL.11 NO.2 | FEBRUARY 2014 | 119 [2] 2.2 Measures of the Location of the Data - OpenStax
Why quartiles are useful
Quartiles are less affected by extreme values, called outliers, than the mean and standard deviation are. Because of that, they are often helpful when data are skewed, irregularly shaped, or contain extreme outliers. The IQR can also help flag possible outliers: values below Q1 − 1.5×IQR or above Q3 + 1.5×IQR are suspected and need further investigation. [source 0, source 1]
[1] nature methods | VOL.11 NO.2 | FEBRUARY 2014 | 119 [2] 2.2 Measures of the Location of the Data - OpenStax
Limits and cautions
There is no single universal method for calculating quartiles; software may use different rules, such as simple averaging, linear interpolation, or even box boundaries based on hinges rather than quartiles. Box-plot boundaries can therefore differ across programs. Also, quartiles describe a sample and are estimates, so sample variability affects the plot. In research, grouping continuous data into quartiles can hide detail and make comparisons across studies harder. [source 0, source 2]
[1] nature methods | VOL.11 NO.2 | FEBRUARY 2014 | 119 [3] Against quantiles: categorization of continuous variables in ... - PMC
SEE THE IDEA
How quartiles summarize ordered data
Put values from smallest to largest before finding quartiles.
Use the 25th, 50th, and 75th percentiles as cut points.
Compute Q3 − Q1 to describe the middle 50% spread.
Draw a box from Q1 to Q3 with the median marked inside.
Each step uses the previous one: sorting enables quartiles, quartiles define the IQR, and these values build a box plot.
Quartiles are ordered-data landmarks that support summaries of center, spread, and possible outliers. [source 0, source 1]
TRY IT YOURSELF
Test your understanding
Choose an answer, then check the explanation.
PUT IT TOGETHER
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Sources and further reading
This general lesson was generated from public source material. It explains a concept; it does not interpret a private paper or provide medical advice.