Univariate statistics provide information on a single variable. They summarise and reveal patterns in that variable. In Source, the variable used to calculate statistics is a time series result.
The types of univariate statistics available in Source are described in Table 1.
Table 1. Univariate Statistics
Statistic | Definition | Example for |
|---|---|---|
Minimum | Minimum value in the time series | 0 |
Maximum | Maximum value in the time series | 9 |
Number of Values | The number of values in the time series, not including nulls | 6 |
Number of Nulls | The number of nulls, either missing values or values entered as -9999. These values are ignored in all other univariate statistics. | 1 |
Total | The sum of all values in the time series. | 27 |
Mean | The sum of all values in the time series divided by the number of values. See Mean for more information. | 5 |
Median | The middle value in the sorted list of all values in a time series. For n values, the middle value is n+12. When n is even, the median is the mean of the two middle values. | 4 |
Standard Deviation | How widely values in the time series vary from the mean. See Standard Deviation for more information. | 3.89 (to 2 decimal places) |
Skew | The skewness of the distribution of values in the time series. See Skew for more information. | 0.23 (to 2 decimal places). |
Standard Deviation
Definition
The standard deviation (s) measures the amount by which values in the time series vary from the mean. It is defined as:
Equation 1 | s= i=0nxi-x2n-1 |
Where:
x is the value of time series x at time step i
x is the mean of time series x
n is the number of values in time series x.
Interpretation
A low (smaller) standard deviation, indicates the values are close to the mean, with a narrow range; a high standard deviation indicates the values are spread out over a wider range.
Skew
Definition
The skew measures the degree of asymmetry of a distribution around its mean. It is defined as:
Equation 2 | skew= n(n-1)(n-2)i=0nxi-xs3 |
Where all terms are defined in Equation 1.
Interpretation
A symmetrical dataset will have a skew of 0. A positive skew indicates a distribution with an asymmetric tail extending toward values greater than the mean. Negative skew indicates a distribution with an asymmetric tail extending toward values less than the mean.