generic_user - 4 years ago 122
R Question

# "circular" mean in R

Given a dataset of months, how do I calculate the "average" month, taking into account that months are circular?

``````months = c(1,1,1,2,3,5,7,9,11,12,12,12)
mean(months)
## [1] 6.333333
``````

In this dummy example, the mean should be in January or December. I see that there are packages for circular statistics, but I'm not sure whether they suit my needs here.

I think

``````months <- c(1,1,1,2,3,5,7,9,11,12,12,12)
library("CircStats")
conv <- 2*pi/12 ## months -> radians
``````

Now convert from months to radians, compute the circular mean, and convert back to months. I'm subtracting 1 here assuming that January is at "0 radians"/12 o'clock ...

``````(res1 <- circ.mean(conv*(months-1))/conv)
``````

The result is -0.3457. You might want:

``````(res1 + 12) %% 12
``````

which gives 11.65, i.e. partway through December (since we are still on the 0=January, 11=December scale)

I think this is right but haven't checked it too carefully.

For what it's worth, the `CircStats::circ.mean` function is very simple -- it might not be worth the overhead of loading the package if this is all you need:

``````function (x)
{
sinr <- sum(sin(x))
cosr <- sum(cos(x))
circmean <- atan2(sinr, cosr)
circmean
}
``````

Incorporating @A.Webb's clever alternative from the comments:

`````` m <- mean(exp(conv*(months-1)*1i))
12+Arg(m)/conv%%12  ## 'direction', i.e. average month
Mod(m)              ## 'intensity'
``````
Recommended from our users: Dynamic Network Monitoring from WhatsUp Gold from IPSwitch. Free Download