The Mutually Exclusive and Collectively Exhaustive (MECE) framework is a powerful concept that is popular amongst consultants and consulting interviews. Whilst you will never be asked questions about it directly, you will be expected to apply it when appropriate with confidence.
The MECE framework is applicable when categorizing information such as demographics, processing data, formulating problem statements and making estimations. Market sizing questions are common in interviews for consulting as they require logical thought, common sense and basic math skills. In order to reach a comprehensive and reasonable answer to these questions, it is often important to apply the MECE framework at one or more of the steps.
So, what does it mean to be mutually exclusive and collectively exhaustive?
Definition
A statistical term describing two or more events that cannot occur simultaneously.
Example 1
When rolling a dice there are six possible outcomes, the numbers 1-6. However, in a single roll you cannot role a 3 and a 5 it can only be one number. This is because these events are mutually exclusive.
Example 2
When considering the number of people in the UK that play badminton once per year, you may choose to categorise the population by age. Perhaps something like this:
{0-10, 10-20, 20-30, 30-40, 40-50, 50+}
Is this mutually exclusive?
No, this is not mutually exclusive because there are overlaps in these categories. For instance, someone who is 20 will be counted twice as they fall at the top end of the second age group but also the bottom end of the third group. These overlaps prevent this categorization from being mutually exclusive.
Definition
A set of events is collectively exhaustive if they cover all the probability space, i.e. the probability of anyone of the events happening is 100%.
Example 1
In the case of rolling a dice, categorizing the outcomes as {1,2,4,5,6} isn’t collectively exhaustive as it is possible the event of rolling a fair, six-sided dice results in a 3 and this hasn’t been accounted for.
Example 2
For pople in the UK playing badminton, you could categorise the population as the following:
{10-20, 21-30,31-40,41-50}
Is this collectively exhaustive?
No, this would not be collectively exhaustive as the population aged 0-9 and 51+ have been excluded, and it is possible that there are people in these age categories that play badminton.
Question
Estimate the number of people in the UK that play badminton at least once a week.
Using the MECE framework:
Answer
Our final estimate for the number of people in the UK that play badminton at least once a week is 700,000.
Tip: Use numbers that are easy to calculate in your head, such as a UK population of 60 million, when in fact the UK population is approximately 66 million people.
To practice applying the MECE framework, the best way to do so is with our 50 market sizing questions that are available for download.
