Quartiles
Quartile is Latin and literally means quarter value. Quartiles divide a sorted data series into four (approximately) equal sections.
The first quartile (abbreviated Q1) divides the sorted data series into the lower quarter and the upper three-quarters.
The second quartile is the median.
The third quartile (abbreviated Q3) divides the sorted data series into the lower three-quarters and the upper quarter.
The following applies for:
Q1: At most one quarter of the observations are smaller than Q1 and at most three quarters of the observations are larger than Q1.
Q3: At most three quarters of the observations are smaller than Q3 and at most one quarter of the observations are larger than Q3.
Boxplots
A boxplot is used to graphically represent the distribution of data points in a series. It is a summary of the five position parameters of a data series and consists of the:
Minimum (smallest value)
Q1
Median
Q3
Maximum (largest value)
Components of a boxplot (in vertical orientation)
The boxplot consists of the box, and the upper and lower antennas. In the box, a horizontal line marks the median. The upper edge of the box lies on the third quartile, the lower on the first quartile. The end of the upper antenna marks the maximum. The end of the lower antenna marks the minimum.
A boxplot thus clearly represents the distribution of the data around the median, broken down into quartiles: About 50% of the data lie within the box, about 25% above the box, and about 25% below the box. The width of the box indicates whether the middle half of the data lie more near the median or more dispersed from it. The smaller the box, the more concentrated the middle half of the data is around the median. The location of the median in the box indicates whether the middle half of the data is concentrated on one side of the median. The shorter one side of the box is compared to the other side, the more the middle half is concentrated on that side of the median.