1.8 Graphical Representations of Summary Statistics

This section represents summary statistics for quantitative data graphically.   Describing summary statistics we can use it to talk about our data in the context.

Boxplots are excellent displays to detect the outliers. John Tukey, in the 1970s, divided data into four equal parts, 25 % in each section, and drew a boxplot through it. This five summary display reports its median, 1st and 3rd quartiles, minimum and maximum. Once you have all these values, you will be able to construct the boxplot. Using IQR, we can erect fences to detect the outlier in our data. For soft outliers, use 1.5  and 3 for stronger (far) outliers. Multiply the coefficient with IQR add to Q3 to detect the outlier on the upper side of data and subtract from Q1 to do so for the lower side.

Upper fence = Q3 + 1.5 IQR

and

Lower fence = Q1 - 1.5 IQR

The fences are not included in the boxplot, but it helps us to draw the whiskers of the boxplot. Any number beyond the whiskers will be displayed in asterisk, indicating that those values are outliers, something that we could hardly know from other quantitative displays. 

Boxplot can help us find important features about the distribution. The central box stretches from Q1 to Q3 and shows the middle (50%) of data. If the median (Q2) is situated in the right middle of the quartiles, then the box will look symmetric. However, we should also look at whiskers. If the whiskers have different lengths, the distribution will be skewed on to the longer whisker’s side.