Anyone who is preparing to take the Project Management Professional (PMP)® exam will be aware that there are a handful of formulae to be learned. Most of these relate to earned value management and estimating. However there is one that stands alone and, as such, is often forgotten. I’m referring of course to the number of communication channels in a project.
Forgetting this is not the end of the world. If all goes to all, you can answer the question by going back to first principles. If you have one person with you on the team, then there is only a single, bi-directional channel. However, if you add another person to the team, the original channel is still in place, but both of you now have to open bi-directional channels to the newcomer, bringing the total to three, and so on.
It does not take long to work out the general formula of N * (N – 1) / 2. Think of it like this: if there are N people on the team, each of them has to open N – 1 channels so they can communicate with everyone else. This gives us the N * (N – 1) bit which gives us the total number if uni-directional channels. Just divide by two to get the bi-directional count.
It is very unusual for the Project Management Institute to put a question like this into the PMP® exam: “There are 10 people on the team, how many communication channels are there?” This is too easy (it is 10 * 9 / 2 = 45). A more typical question would be: “You acquired 10 people originally for your project. But 2 more were hired to help with the quality control effort. How many extra communication channels have been added?”
Qualified PMPs® and those who have practiced trial PMP® exams during their PMP® training will spot the trap in this question straight away: there actually were 11 people on the team at the start. Remember your own role as the project manager! So the normal approach to the question is to calculate the original number of channels (11 * 10 / 2 = 55). Then calculate the new number of channels (13 * 12 / 2 = 78) and subtract the original (78 – 55 = 23).
For most PMP® exam students, this works perfectly well, but it is an interesting exercise to do a bit of basic algebra here, because it yields a useful shortcut. Suppose we have N members on our original team and a new person is added, what happens to the number of communication channels?
Well the formula is the number of channels for the new team ((N + 1) * ((N + 1) – 1) / 2) minus the number of channels for the original team (N * (N – 1) / 2). Putting this all on one line gives:
[((N + 1) * N) – (N * (N – 1))] / 2
= (N2 + N – N2 + N) / 2
= 2N / 2 = N
So, the number of new channels added when you add a new team member is equal to the original number of team members.
Now, faced with the previous question, we can say: the original number of team members was 11, so adding a team member adds 11 new channels. If we add another team member to these 12, the number of new channels is 12. Add these together and you get the total number of new channels, which is 23, as before.
Put more formally: if N is the original team size and N + n is the new team size, the number of new channels is the sum of all integers between N and N + n inclusive.
The interesting point to all this is that the bigger the team, the bigger the consequences of adding to it. In the agile world, it is recommended that teams should be seven plus or minus two in size. The goal is to incorporate all the skills necessary to carry out the project work but, at the same time, keep it small enough to prevent cliques forming and to keep communication manageable. Your PMP® training did not talk about planning, managing and monitoring communication just to make the PMP® exam more difficult – communication is a vital part of any project.
To learn more about Project Communication Management, consider one of Velopi’s PMP® Exam Preparation courses. These are held online in our virtual classroom. Find out more by visiting our training page or by contacting us directly.
By Velopi Seamus Collins