Definition:Directional Data
Definition
Directional data is data which consists of angular coordinates from a given point.
Also known as
Directional data is also known as:
Examples
Arbitrary Example $1$
Consider the following set of directional data measured over the range $0 \degrees$ to $360 \degrees$:
- $\set {1 \degrees, 5 \degrees, 10 \degrees, 350 \degrees, 355 \degrees, 359 \degrees}$
If this were treated as linear data, the arithmetic mean and median are both $180 \degrees$.
However, if this directional data was measured with the same zero, but with a range from $-180 \degrees$ to $+180 \degrees$, it becomes:
- $\set {1 \degrees, 5 \degrees, 10 \degrees, -10 \degrees, -5 \degrees, -1 \degrees}$
which gives a arithmetic mean and median of $0 \degrees$.
By visual inspection, it is apparent that the second of these is a more sensible interpretation of centrality
Arbitrary Example $2$
Let points be distributed on the circumference of circle such that the probability of an arbitrary point lying on a given arc of a given length is the same.
Then there is a uniform directional distribution:
In such a case, there is no unique arithmetic mean.
Also see
- Results about directional data can be found here.
Sources
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): directional data (angular data, circular data)