Statistical Characteristics of Hydrologic Time Series - Hydrologic Time Series Analysis: Theory and Practice - page 21

values, where CV values of 0-15, 16-35 and >36 indicate little, moderate and
high variability, respectively. Typical ranges of CV values of salient soil
properties are reported in the literature (Jury, 1986; Jury et al., 1987; Beven
et al., 1993; Wollenhaupt et al., 1997).
One robust estimator of spread other than the IQR, being more resilient to
outliers in a dataset than the standard deviation, is the median absolute deviation
(MAD). In the standard deviation, the distances from the mean are squared, so
on an average, large deviations are weighted more heavily, and thus outliers
can heavily influence it. In the MAD, the magnitude of the distances of a
small number of outliers is irrelevant. The MAD is computed by first creating
a new difference time series by listing the absolute value of differences | d |
between each data value and median of a time series.

| d i | = x i - P 50 (13)

where P 50 = median of the original time series.
Thereafter, the MAD is computed as the median of the absolute difference
time series as follows:

MAD = P 50 | d | (14)

Quartile coefficient ( qc ) of dispersion is another descriptive statistic which
measures dispersion and is used to make comparison within and between
datasets. The test-statistic is computed using the first ( P 25 ) and third ( P 75 )
quartiles for each data set. The quartile coefficient of dispersion ( qc ) is given
as:

PP
PP

75 25

qc = (15)

75 25

2.3 Measures of Skewness

Hydrologic time series data are usually skewed, which means that data in the
time series are not symmetric around the mean or median, with extreme
values extending out longer in one direction. The probability density function
for a lognormal distribution shown in Fig. 2.4 demonstrates this skewness in
the data. When extreme values extend the right tail of the distribution (as
shown in Fig. 2.4), the distribution of time series data is said to be skewed to
the right, or positively skewed. Whereas, when extreme values extend the left
tail of the distribution, the time series data are said to be skewed to the left, or
negatively skewed. For the skewed data values, the mean is not expected to be
equal to the median, but is pulled toward the tail of the distribution. Thus, for
the positively skewed data, the mean exceeds more than 50% of the data (Fig.
2.4). The standard deviation is also inflated by data in the tail. In hydrology,
all kinds (e.g., rainfall, streamflow, groundwater levels, etc.) of time series