the data is skewed to the left ( negatively skewed).

the value 0.5 is an 'extreme' outlier, more than 3*(IQR) below Q1.

the value 3.5 is a 'mild' outlier, between 1.5*(IQR) and 3*(IQR) below Q1.

smallest non-outlier observation = 5 (left 'whisker').It is worth noting that a boxplot may be constructed in a similar manner vertically as opposed to horizontally by merely interchanging 'left' for 'bottom' and 'right' for 'top' in the above description.Ī plain-text version might look like this:.Add an appropriate label to the number line and title the boxplot.'Mild' outliers - that is, those observation which lie more than 1.5 times the IQR from the first and third quartile but are not also extreme outliers are indicated by the presence of a closed dot. 'Extreme' outliers, or those which lie more than three times the IQR to the left and right from the first and third quartiles, respectively, are indicated by the presence of an open dot. Indicate outliers by open and closed dots.Likewise, indicate where the largest value that is not an outlier is by a 'whisker', and connect that whisker to the box via another horizontal line. Indicate where the smallest value that is not an outlier is by a vertical tic mark or 'whisker', and connect the whisker to the box via a horizontal line. Any data observation which lies more than 1.5*IQR lower than the first quartile or 1.5*IQR higher than the third quartile is considered an outlier.Indicate where the median lies inside of the box with the presence of a symbol or a line dividing the box at the median value.The box may be as tall as one likes, although reasonably proportioned boxplots are customary. 25) and on the right by the third quartile (x. Construct a box above the number line bounded on the left by the first quartile (x.

Calculate the interquartile range (IQR) by subtracting the first quartile from the third quartile.

Calculate the median, first quartile (x.

Boxplots can be drawn either horizontally or vertically.įor a data set, one constructs a boxplot in the following manner: The spacings between the different parts of the box help indicate variance, skew and identify outliers. The boxplot was invented in 1977 by American statistician John Tukey.īoxplots are able to visually show different types of populations, without any assumptions of the statistical distribution. In descriptive statistics, a boxplot (also known as a box-and-whisker diagram or plot or candlestick chart) is a convenient way of graphically depicting the five-number summary, which consists of the smallest observation, lower quartile (Q1), median, upper quartile (Q3), and largest observation in addition, the boxplot indicates which observations, if any, are considered unusual, or outliers. Box Plot of Data from the Michelson-Morley Experiment.

Box and whisker plot definition