What is Quartile?

The values at the positions that divide data sorted by size into four equal parts, called from the smallest the first quartile, the second quartile (the median) and the third quartile. The interquartile range, the third quartile minus the first, is the width containing the middle half of the data and is a measure of spread little affected by outliers. A box plot shows the quartiles as a box and the minimum, maximum and so on as whiskers, making the shapes of distributions easy to compare. There are several conventions for computing quartiles, and the values differ slightly between methods.

Japanese name: 四分位数

Quartile appears in 1 practice question across 1 topic, including Probability, Statistics and Queueing.

Field: Probability, Statistics and Queueing

Try it: questions about Quartile

The 11 data values 1, 3, 4, 6, 7, 8, 10, 12, 13, 15, 20 are shown in a box plot. The first and third quartiles are taken as the medians of the lower and upper halves of the data, excluding the median. Which of the following is the interquartile range, which corresponds to the length of the box?

A4.5
B9
C19

Show answer and explanation

Answer: B. 9

The median is the sixth value, 8. The median of the lower half 1, 3, 4, 6, 7 is 4, the first quartile, and the median of the upper half 10, 12, 13, 15, 20 is 13, the third quartile, so the interquartile range is 13 − 4 = 9. A box plot draws a box from the first to the third quartile with a line at the median, showing where the middle half of the data lies. There are several conventions for computing quartiles, and the functions of spreadsheet software and the like may give slightly different values.

Quartile in the explanations

The median of the lower half 1, 3, 4, 6, 7 is 4, the first quartile, and the median of the upper half 10, 12, 13, 15, 20 is 13, the third quartile, so the interquartile range is 13 − 4 = 9.
The 11 data values 1, 3, 4, 6, 7, 8, 10, 12, 13, 15, 20 are…

Questions that mention Quartile (1)

The 11 data values 1, 3, 4, 6, 7, 8, 10, 12, 13, 15, 20 are shown in a box plot. The first and third quartiles are taken as the medians of the lower and upper halves of the data, excluding the median. Which of the following is the interquartile range, which corresponds to the length of the box?

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