Circular Data
- Represents angles or directions with values between 0 and 360 degrees.
- Common in meteorology, astronomy, and geography (e.g., wind direction, compass direction).
- Requires specialized statistics (circular mean, circular standard deviation) because values near the 0/360 boundary wrap around.
Definition
Section titled “Definition”Circular data is a type of data represented by values that range between 0 and 360 degrees, commonly used to represent angles and directions in fields such as meteorology, astronomy, and geography.
Explanation
Section titled “Explanation”Circular data encode directions or angles on a circular scale from 0 to 360 degrees. Because the scale wraps around (0 degrees adjacent to 360 degrees), conventional linear statistics can give misleading results for measures of central tendency and dispersion. To account for this, specialized statistical methods are used.
Circular mean (also called circular average) and circular standard deviation are two such methods. Both procedures convert circular data values into complex numbers, operate on those complex numbers (for example, taking an average or computing a standard deviation), and then convert the result back into a circular value. These approaches allow for correct handling of values that are close to the 0 and 360 degree boundaries.
Examples
Section titled “Examples”Wind direction
Section titled “Wind direction”In meteorology, wind direction is typically measured in degrees and ranges from 0 to 360. For instance, a wind direction of 0 degrees indicates a wind coming from the north, a wind direction of 90 degrees indicates a wind coming from the east, and a wind direction of 180 degrees indicates a wind coming from the south.
Compass direction
Section titled “Compass direction”In geography and navigation, compass direction is typically measured in degrees and ranges from 0 to 360. For instance, a compass direction of 0 degrees indicates a direction towards the north, a compass direction of 90 degrees indicates a direction towards the east, and a compass direction of 180 degrees indicates a direction towards the south.
Use cases
Section titled “Use cases”- Calculating average direction and variability for wind direction to inform weather analysis.
- Supporting decisions about activities such as farming or outdoor recreation by summarizing directional patterns.
- Any application in meteorology, astronomy, or geography that involves angular measurements.
Notes or pitfalls
Section titled “Notes or pitfalls”- Values near the boundaries should be treated as adjacent: for example, 359 degrees is considered to be very similar to 1 degree despite being far apart numerically on a 0 to 360 scale.
- Conventional linear statistics can misrepresent central tendency and dispersion for circular data; use circular mean and circular standard deviation instead.
Related terms
Section titled “Related terms”- circular mean
- circular standard deviation