Although, generally speaking, project managers are not expected to demonstrate complicated mathematical and / or statistical capabilities, there are some aspects of both these disciplines where basic knowledge and understanding of some basic concepts can enhance the project managers’ ability to perform fundamental project management duties – primarily around risk management.

The Project Management Body of Knowledge advocates the use of “Monte Carlo Simulation” within the context of performing quantitative risk assessment analysis. Although in most cases, executing such analysis will require the invocation of some sort of automated software tools, it is important for the project manager to understand the key principles behind the mathematical and statistical analysis performed by this sort of tools.

Today’s post will focus on three basic concepts (all of which, funnily enough, start with the letter ‘M’):

  • Mean
  • Median
  • Mode

The Mean

The mean (or average) of a set of data values is the sum of all of the data values divided by the number of data values. That is:

image

Using mathematical symbols, the above equation will look as follows:

Where:

  • X is the mean of the set of x values
  • is the sum of all x values in the set
  • n is the number of x values in the set

For example:

A project schedule consists of 10 tasks, with the following estimated durations:

Task ID Estimated Duration (days)
1 3
2 4
3 5
4 6
5 3
6 7
7 4
8 5
9 2
10 4

Based on the above:

  • Sum of all data values = 3 + 4 + 5 + 6 + 3 + 7 + 4 + 5 + 2 + 4 = 43 days
  • Number of data values = 10
  • The mean = 43 / 10 = 4.3 days

The Median

The median of a set of data values is the middle value of the data set after it has been arranged in an ascending order.

Median = ½ (n + 1)th value in a set, where: n is the number of data values in the set

Note: If the number of values in the set is even, the median is calculated as the average of the two middle values.

For example:

The above task list, ordered in an ascending order, will look as follows:

Task ID Estimated Duration (days)
9 2
1 3
5 3
2 4
7 4
10 4
3 5
8 5
4 6
6 7

Given that there are 10 tasks in this list, the then ½(10+1) = 5.5.

Given that in this case n = 10, the median will be calculated as the average between the two middle values (being tasks 7 & 10) = (4 + 4) / 2 = 4 days.

The Mode

The mode represents a data value that appears most frequently within a set of values. Obviously if one or more values appear in exactly the same frequency, all such values will be considered to be part of the set Mode.

For example:

Given the following set of numbers: 1, 2, 3, 2, 3, 4, 1, 3; the number 3 appears the most times and is therefore the Mode.

To Summarize:

  • Mean = average value
  • Median = middle value
  • Mode = most often occurring value

Easy?

Stay tuned for the next installment as things will get slightly spicier.

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