Methods for Testing Normality of Hydrologic Time Series - Hydrologic Time Series Analysis: Theory and Practice - page 35

stem-and-leaf plot of normally distributed data should be close to bell shaped.
Also, the data distribution displayed by the stem-and-leaf plot may be used to
assess skewness or symmetry of the data. The top half of the stem-and-leaf
plot should be a mirror image of the bottom half of the stem-and-leaf plot for
symmetric data distribution. The data that are skewed to the left will have the
higher data density in the top half of the plot and less data density over the
bottom half of the plot. Consider a hydrologic time series X 1 , X 2 , ..., X n with
n data points. To develop a stem-and-leaf plot, following steps are used:
Step 1: Arrange n data points of time series in order of increasing magnitude
from the smallest to the highest. The ordered data are generally labelled
(from smallest to largest) as X (1) , X (2) , ..., X (n) .
Step 2: Decide either one or more of the leading digits to be the stem values.
As an example, for the value 236, 2 could be used as the stem value
as it is the leading digit.
Step 3: List the stem values from smallest to largest at the left (along a
vertical axis). Enter the leaf (the remaining digits) values in order
from lowest to highest to the right of the stem. Using the value 236
as an example, if 2 is the stem then 36 will be the leaf.
3.1.3 Box and Whisker Plot
A 'box and whisker plot' or simply 'box plot' is a schematic diagram (Fig.
3.4) used for visualizing important statistical quantities (such as quartiles) of
the time series data. Box plots are useful in situations where it is not necessary
or feasible to depict all the details of a time series distribution. The box and
whisker plot consists of a central box with a square or a line in the box and
two lines extending out from each end of the box called whiskers . The square
or line within the box represents the median (USEPA, 1996; USEPA, 2006).
Fig. 3.4. Example of a Box and Whisker plot.
The bottom and top horizontal lines in the box in a 'box and whisker plot'
indicate the 25 th and 75 th percentile, respectively, of the statistics computed
from the observed data. The length of the central box indicates the spread of