"What you thought was a 5-minute survey actually cost your client $100,000. Here's how to avoid that."

POV: You run a B2E (business-to-enterprise) consulting firm. Your current client is a 10,000 employee company that's asked you to come up with a strategy to boost employee morale and also reduce last minute absences from employees.

To develop such a strategy, you first need to understand why morale is low and why last minute absences are so prevalent. I.e. you need to develop some empathy with your client and their employees so that you can propose a solution that will actually work for them. But how do you develop empathy with 10,000 employees?

You could start by sending a 5-minute survey to every employee. Given the psychological distraction of task-switching, that means a 5-minute survey will probably cost at least 10 minutes of lost productivity. 10 minutes of lost productivity multiplied by 10,000 employees is 100,000 minutes of productivity lost for the company. 1667 hours. Over 208 days of full-time effort lost. There are 250 workdays in a year, so that's over 83% of an entire employee-work-year of productivity loss. If the typical employee makes $100,000/year, then after employer taxes, healthcare costs, etc, a typical employee likely costs at least $120,000/year. 83% of that is $99,600. In other words, your 5-minute survey has cost your client about $100,000. To add insult to injury, a 5-minute survey may help you identify possible problems that cause low employee morale, but it likely doesn't give you quite enough to really understand the problem. You'll have to send more surveys or conduct employee interviews later.

The problem with helping large enterprise clients solve large internal problems is that even diagnosing the problem can cost the the client a lot of money. However, it doesn't have to. I'm going to teach you a dirt simple statistical trick that will allow you to answer lots of questions with minimal time & cost to your client. Not only will your consulting services be less intrusive, you'll also be able to ask way more questions.

The rule of 5

The trick is called the rule of 5.

Suppose you hypothesize that employee morale may be low because many employees are stressed out parents with young kids. Maybe adding daycare could boost morale and also decrease last minute call-outs caused by childcare issues?

You'd like to find out whether a lot employees actually do have kids under the age of 6 who are in need of better childcare. However, the employee database doesn't track whether any particular employee is a parent. Here's what you can do.

Start pulling random employees from the database. For each employee, shoot them a Slack / Microsoft Teams message asking if they are a parent. If so, ask them the age of their youngest kid. Repeat until you have 5 employees who respond that they are a parent and provide the answer of youngest child's age.

Suppose the answers you get are 2 years, 2 years, 5 years, 1 year, and 6 years old.

Look at the lowest (1 year old) and highest (6 years old) of the 5 answers. There is a 93% chance that the median age of the youngest child of employee-parents is in that range. In other words, from just a few unintrusive Slack messages, you now know with high confidence that at least half of parents working for the company have a child aged 1-6 years old. Impressive! Company childcare might really help! It might now be worthwhile to send out some surveys.

How to use the rule of 5

The rule of 5 is an extremely general technique to estimate the average value (median) of any variable. Here is the distilled procedure:

1. Randomly sample 5 people or things you want to know about (e.g. employees who are also parents)
2. Record the value of a variable you care about for each sample (e.g. the age of youngest child)
3. Find the minimum and maximum value of the 5 results

If you follow those three steps, there is a greater than 93% chance that the minimum-to-maximum range you found in step 3 contains the median value of the variable you care about.

Why does the rule of 5 work?

The median is a special number: half of results are above it and half below it. That means each sample you collect is a coin flip: 50% chance it is above the median and 50% chance it is below the median. The chance of not sampling anything above the median 5 times in a row is then the same chance as flipping a coin 5 times and getting heads every time: (0.5)^5 = 0.03125 (.e. 3.125%).

The chance of sampling 5 times and not getting anything below the median is the same: 0.03125

That means that the chance of a random sample of 5 containing at least one value above the median and one value below the median is

0.9375 = 1 - 0.03125 - 0.03125

I.e. 93.75%

This works whether you are sampling 5 employees from 10,000 or 5 cans in a warehouse from 1,000,000.

Some additional example use cases

The rule of 5 is useful to estimate the average value of all sorts of things in business. Here are some additional examples:

• The expiration date of cans on the shelves of a grocery store
• Order size of purchases through an e-commerce website
• Age of a bar's customers (e.g. if the bar wants to tailor its marketing to the demographics of its existing customer base)
• The typical price of various competitors' products at a retail store
• How the average employee at a company would rate the competence of their boss on a scale from 1-10 (variations of this can be extremely useful ways to quickly gauge employee sentiment about various aspects of their work experience, even in huge organizations with tens of thousands or hundreds of thousands of employees)