Statistics#
The statistics catalog tells how the values of a spec were obtained from
the source data. A monthly precipitation total uses sum, a daily mean
temperature uses mean, and values that were never aggregated, such as a
lab analysis or a single station reading, use instant. The catalog ships
with the package and seeds the statistics table when a database is
created. This page is built from the same file.
Percentiles are named pNNN after their level: p000, p001,
p005, then every 5 up to p095, then p099 and p100. The
formula only defines the quantile, so a spec should state its interpolation
method when it matters. Standard deviation and variance are sample estimates,
dividing by \(n-1\).
Name |
Alias |
Title |
Symbol |
Formula |
Abstract |
|---|---|---|---|---|---|
|
|
Arithmetic Mean |
\(\bar{x}\) |
\(\frac{1}{n}\sum_{i=1}^{n}x_i\) |
Average value of a set |
|
|
Cumulative Sum |
\(\Sigma x\) |
\(\sum_{i=1}^{n}x_i\) |
Total sum of all values in a set |
|
|
Minimum Value |
\(x_{\min}\) |
\(\min(x_1,\ldots,x_n)\) |
Smallest value in a set |
|
|
Maximum Value |
\(x_{\max}\) |
\(\max(x_1,\ldots,x_n)\) |
Largest value in a set |
|
|
Instantaneous Value |
\(x(t)\) |
\(x(t)\) |
Value observed at a single moment, without aggregation (eg, a lab analysis or a station reading) |
|
|
Standard Deviation |
\(s\) |
\(\sqrt{\frac{1}{n-1}\sum_{i=1}^{n}(x_i-\bar{x})^{2}}\) |
Spread of the values around the mean, sample estimate |
|
|
Sample Variance |
\(s^{2}\) |
\(\frac{1}{n-1}\sum_{i=1}^{n}(x_i-\bar{x})^{2}\) |
Mean squared deviation from the mean, sample estimate |
|
|
Mode |
\(\hat{x}\) |
\(\arg\max_{x} f(x)\) |
Most frequent value in a set |
|
|
Count |
\(n\) |
\(\sum_{i=1}^{n}1\) |
Number of values in a set |
|
|
0th Percentile |
\(P_{0}\) |
\(\inf\{x : F(x) \geq 0\}\) |
Value below which 0% of the values in a set fall (the minimum) |
|
|
1st Percentile |
\(P_{1}\) |
\(\inf\{x : F(x) \geq 0.01\}\) |
Value below which 1% of the values in a set fall |
|
|
5th Percentile |
\(P_{5}\) |
\(\inf\{x : F(x) \geq 0.05\}\) |
Value below which 5% of the values in a set fall |
|
|
10th Percentile |
\(P_{10}\) |
\(\inf\{x : F(x) \geq 0.1\}\) |
Value below which 10% of the values in a set fall |
|
|
15th Percentile |
\(P_{15}\) |
\(\inf\{x : F(x) \geq 0.15\}\) |
Value below which 15% of the values in a set fall |
|
|
20th Percentile |
\(P_{20}\) |
\(\inf\{x : F(x) \geq 0.2\}\) |
Value below which 20% of the values in a set fall |
|
|
25th Percentile |
\(P_{25}\) |
\(\inf\{x : F(x) \geq 0.25\}\) |
Value below which 25% of the values in a set fall |
|
|
30th Percentile |
\(P_{30}\) |
\(\inf\{x : F(x) \geq 0.3\}\) |
Value below which 30% of the values in a set fall |
|
|
35th Percentile |
\(P_{35}\) |
\(\inf\{x : F(x) \geq 0.35\}\) |
Value below which 35% of the values in a set fall |
|
|
40th Percentile |
\(P_{40}\) |
\(\inf\{x : F(x) \geq 0.4\}\) |
Value below which 40% of the values in a set fall |
|
|
45th Percentile |
\(P_{45}\) |
\(\inf\{x : F(x) \geq 0.45\}\) |
Value below which 45% of the values in a set fall |
|
|
50th Percentile |
\(P_{50}\) |
\(\inf\{x : F(x) \geq 0.5\}\) |
Value below which 50% of the values in a set fall (the median) |
|
|
55th Percentile |
\(P_{55}\) |
\(\inf\{x : F(x) \geq 0.55\}\) |
Value below which 55% of the values in a set fall |
|
|
60th Percentile |
\(P_{60}\) |
\(\inf\{x : F(x) \geq 0.6\}\) |
Value below which 60% of the values in a set fall |
|
|
65th Percentile |
\(P_{65}\) |
\(\inf\{x : F(x) \geq 0.65\}\) |
Value below which 65% of the values in a set fall |
|
|
70th Percentile |
\(P_{70}\) |
\(\inf\{x : F(x) \geq 0.7\}\) |
Value below which 70% of the values in a set fall |
|
|
75th Percentile |
\(P_{75}\) |
\(\inf\{x : F(x) \geq 0.75\}\) |
Value below which 75% of the values in a set fall |
|
|
80th Percentile |
\(P_{80}\) |
\(\inf\{x : F(x) \geq 0.8\}\) |
Value below which 80% of the values in a set fall |
|
|
85th Percentile |
\(P_{85}\) |
\(\inf\{x : F(x) \geq 0.85\}\) |
Value below which 85% of the values in a set fall |
|
|
90th Percentile |
\(P_{90}\) |
\(\inf\{x : F(x) \geq 0.9\}\) |
Value below which 90% of the values in a set fall |
|
|
95th Percentile |
\(P_{95}\) |
\(\inf\{x : F(x) \geq 0.95\}\) |
Value below which 95% of the values in a set fall |
|
|
99th Percentile |
\(P_{99}\) |
\(\inf\{x : F(x) \geq 0.99\}\) |
Value below which 99% of the values in a set fall |
|
|
100th Percentile |
\(P_{100}\) |
\(\inf\{x : F(x) \geq 1\}\) |
Value below which 100% of the values in a set fall (the maximum) |