Viewing Mist-Covered Mountains of Data

A famous classical Chinese poem from the Song dynasty describes the views of a mist-covered mountain called Lushan.

The poem was inscribed on the wall of a Buddhist monastery by Su Shi, a renowned poet, artist, and calligrapher of the 11th century.

Deceptively simple, the poem captures the illusory nature of human perception.
 

   Written on the Wall of West Forest Temple

                                      --Su Shi
 
  From the side, it's a mountain ridge.
  Looking up, it's a single peak.
  Far or near, high or low, it never looks the same.
  You can't know the true face of Lu Mountain
  When you're in its midst.

Our perception of reality, the poem suggests, is limited by our vantage point, which constantly changes.

In fact, there are probably as many interpretations of this famous poem as there are views of Mt. Lu.

Centuries after the end of the Song dynasty, imagine you are traversing a misty mountain of data using the Chinese language version of Minitab 17...

From the interval plot, you are extremely (95%) confident that the population mean is within the interval bounds.

From the individual value plot, the data may contain an outlier (which could bias the estimate the mean).

From the boxplot, the data appear to be extremely skewed (making the confidence interval and mean estimate unreliable).

From the histogram, the data are bimodal (which makes the estimate of the mean utterly ...er...meaningless)

From the time series plot, the data show an order effect, with increasing variation and downward drift.

From the individuals and moving range charts with stages, the data appear stable and in control:

These graphs are all of the same data set.

Take it from Su Shi. Don't rely on a single graphical view to capture the true reality of your data.

Image of Lushan licensed by Wikimedia Commons.