Box plot; third quartile of suspended solids

Box plot

A box plot (box-and-whisker plot) is a graph of the five number summary: minimum, Q₁, median, Q₃ and maximum. It measures the centre (median), spread (IQR and range), skewness and outliers of a data set, and is useful for comparing several groups.

Parts of a box plot

   o                                   (outlier)
          |-----[====|=====]-------|
         min    Q1  median  Q3     max
              |<-- IQR -->|

• Box: from Q₁ to Q₃. It holds the middle 50% of data. Its length is the interquartile range IQR = Q₃ − Q₁.
• Line inside the box: the median. If it is off-centre, the data are skewed.
• Whiskers: lines from the box to the smallest and largest values that are not outliers (within 1.5 × IQR of the box).
• Outliers: points beyond Q₁ − 1.5 IQR or Q₃ + 1.5 IQR, drawn as separate dots.

Third quartile of suspended solids

Order the 11 values:

12, 14, 19, 20, 21, 28, 29, 30, 55, 63, 65

Q₃ is at position 3(n + 1)/4 = 3 × 12/4 = 9, which is the 9th value. (The median of the upper half 29, 30, 55, 63, 65 gives the same result.)

Q3 = 55 ppm

Interpretation: 75% of the days had suspended solids of 55 ppm or less, and only 25% of days were above 55 ppm. The high values (55, 63, 65) show a right-skewed pattern in the river's pollution.