Directional Data/Examples

Examples of Directional Data

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.