A story for water supply engineers depicting problems arising from believing in the law of averages

In April 2014, LeeAnne was shocked.

The tap water was reddish.

LeeAnne lived in Flint City (Michigan state, USA).

She had 4 children.

There were some peculiar observations.

Everyone in the house had a hair fall problem. One of them had rashes on his skin. And another of her children had stopped growing.

She was alarmed.

Let’s go back a bit.

Flint got its water from the city of Detroit. For this, they paid water bills.

Officials were worried about the bills. They were looking for cheaper options.

They found one option and started building pipelines for the new supplier.

The older supplier gave a notice period and cut water after that.

So, temporarily, Flint needed water from somewhere else.

They decided to take it from the Flint River (yes, the city and the river have the same name).

Taking water from the river was not seen as a problem. The city used to get its water from this river before 1960.

Flint City switched to river water in April 2014.

The nature of the river water was different.

The river water had bacteria. Some people reportedly fell ill.

To solve this problem, the city’s authorities added chlorine to the water. This is done in many cities across the world.

But this gave birth to another problem.

In Flint City, many pipelines were made of lead. The lead pipes were rusted from the inside.

This was not a problem: the rust prevented lead from mixing in the water.

But when they switched to river water, the higher level of chlorine cleaned the rust up – this was why the water turned reddish.

And then, lead started mixing with the water.

The metal lead is harmful to humans – above a certain limit.

LeeAnne’s family’s problems – hair fall, rashes, stunted growth, etc – were happening because of lead poisoning.

She was not alone.

Many residents from the city complained about similar problems.

Hearing complaints from many citizens, the city decided to test the water. They collected samples and sent them to labs.

The results came in: the lead in the water was within safe limits.

The authorities asked the people to ‘relax’.

But the problems did not go away. The sheer number of people complaining was too high to ignore.

The citizens took the matter into their own hands.

Many bought testing kits and sent water from their homes to testing labs.

The lab reports said the lead in the water was dangerously high.

How is that possible? Why did the city declare the water safe?


In Flint City, many areas have old pipes – made of lead.

And many areas have newer pipes – not made of lead.

When testing, they should have measured water from the areas with lead pipes.

Turns out, they did not know where the lead pipes were. So they randomly took samples from many areas.

Some samples contained very high lead. Some samples contained zero lead.

Average that. You get a low number.

So the water was said to have low levels of lead.

This story demonstrates this quote well – “never cross a river that is 4 feet deep on average”.

These words have been recently made popular by author N N Taleb.

The idea is this: someone says a river is 4 feet deep on average. Most people are more than 5 feet tall. So, crossing such a river should be okay.

But the catch is this – 4 feet deep on ‘average’.

The actual depth of the river can be much lower as well as higher than 4 feet in different parts.

It could be 1 foot deep in certain parts and 7 feet deep in other parts. The average depth is still 4 feet.

But the maximum depth is 7 feet. Enough to drown most people.

 We should not ask for the average depth of the river. We should ask for the maximum depth of the river.

The study material for AMIE/Junior Engineer exams is available at https://amiestudycircle.com