Module 2 — Mean vs Median

Why Averages Can Hide Operational Reality

What Can an Average Mean?

In healthcare analytics, averages are everywhere.

We regularly see:

average Length of Stay (LoS)
average waiting times
average cost per patient
average ED attendances
average theatre utilisation

Averages are useful because they simplify complex information into a single number that is easy to communicate and compare.

But healthcare systems are rarely “average”.

Behind a single average often sits:

significant variation
operational complexity
long-tail demand
very different patient experiences

Averages simplify reality — but they can also obscure it.

Why This Matters in Healthcare

Suppose two Trusts report the following:

Trust	Average Length of Stay
Trust A	5.1 days
Trust B	7.2 days

At first glance, Trust B may appear less efficient.

But is that comparison fair?

What if Trust B:

serves an older population
has higher frailty prevalence
has more patients with multiple long-term conditions
experiences delayed discharges due to social care pressures
operates a tertiary specialist service
has limited community capacity

The average alone does not tell us this.

This is one of the most important principles in healthcare analytics:

Averages summarise data — but they do not explain it.

Mean vs Median

Two commonly used “averages” are:

Measure	What it represents
Mean	The arithmetic average across all patients
Median	The middle patient when values are ordered

The mean is sensitive to extreme values (outliers).

The median is often more stable and better reflects the “typical” patient experience.

Why Mean and Median Diverge

Imagine ten patients stay in hospital for:

2, 2, 2, 3, 3, 3, 4, 5, 6, 35

Most patients stay only a few days.

But one very long-stay patient changes the average dramatically.

Measure	Result
Mean	6.5 days
Median	3 days

The median helps understand the typical patient. The mean helps understand overall system burden and resource use.

In healthcare:

both matter — but for different reasons

Example — Length of Stay (LoS)

Length of Stay data is usually heavily right-skewed. The example below shows how mean and median can diverge across different patient groups.

This means:

most patients stay a relatively short time
a small number stay much longer
those long stays pull the mean upward

For example:

Patient Group	Mean LoS	Median LoS
All Patients	6.6 days	3 days
Patients aged 65+	7.9 days	3 days
Moderate/severe frailty	10.8 days	4 days
Multiple long-term conditions	12.2 days	4 days

The median patient may stay only a few days.

However, a relatively small number of long-stay patients can account for a disproportionate number of occupied bed days.

Operationally, this matters enormously.

The figure below illustrates why mean and median may tell very different stories in healthcare operational data.

Notice something important:

median LoS changes relatively little, while mean LoS increases substantially as complexity and frailty rise.

This suggests a relatively small number of patients may be driving disproportionate bed occupancy.

Why The Distribution Matters

If we only report the mean:

we lose visibility of variation
we may miss operational bottlenecks
we may misunderstand where pressure originates

Understanding the full distribution helps answer more meaningful operational questions:

Who are our longest-stay patients?
Why are stays prolonged?
Which patients drive bed occupancy?
Are delays clinical, social or pathway-related?
Where would interventions have the greatest operational impact?

Sometimes:

the story is in the shape of the data, not just the average.

Is It Fair To Compare Trusts or ICBs Using Averages?

Averages support benchmarking — but only with context.

Simple comparison may overlook:

population need
frailty burden
pathway complexity
social care pressures

This is why benchmarking should support questions and learning rather than simplistic league tables.

(We explore fair comparison in more depth in Module 5.)

Benchmarking in Practice — Model Hospital

NHS England’s Model Hospital (Model Health System) uses many averages and benchmark metrics including:

average LoS
theatre utilisation
productivity metrics
operational performance indicators

However, Model Hospital also attempts to improve fairness by using:

peer-group comparisons
specialty-level analysis
segmentation
contextual benchmarking

This reflects an important reality:

Healthcare operational benchmarking is inherently complex.

No single metric tells the whole story.

Operational Implications

Averages remain useful.

They help organisations:

summarise performance quickly
benchmark over time
identify broad variation

But averages alone should rarely drive operational decisions.

Waiting Time Example

An average waiting time of:

4 weeks

may sound acceptable.

But if:

most patients wait 1–2 weeks
a smaller group waits 30+ weeks

the average hides an important operational problem.

The average waiting time may look acceptable.

But the patient experience — and operational risk — may not be.

Again:

the shape of the distribution matters.

Key Takeaways

The mean and median measure different aspects of a population
Healthcare data is often skewed rather than normally distributed
A small number of patients can drive disproportionate operational pressure
The median often reflects the “typical” patient experience, while the mean better reflects system burden
The distribution may matter more than the average itself
Fair comparison requires context, not just metrics
Benchmarking should start conversations, not end them

Questions Decision-Makers Should Ask

When reviewing averages:

What does this average actually represent?
How variable is the underlying data?
Are there important outliers?
Are populations comparable?
What operational factors sit behind the numbers?
Does the distribution reveal something the average hides?
What action is realistically possible?