Tags: statistics concept

Mean Median and Mode

Date: 2026-08-16

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Three answers to “what’s typical”, and they only agree when the data is symmetric. The gap between the mean and the median is the fastest read on whether an average is describing anything.

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What they are

• Mean — the sum divided by the count. The balance point
• Median — the middle value when sorted. Half above, half below
• Mode — the most common value

Where they diverge

SYMMETRIC                    RIGHT-SKEWED (order values)

     ╱▔▔╲                    ▌
    ╱    ╲                   ▌▖
   ╱      ╲                  ▌ ▝▖▁▁▁▁▁▁▁▁▁▁
  ────┬────                  ──┬──┬──────────
   mean = median               │  │
   = mode                   median mean
                                    ↑ dragged right by the tail

Mean > median means a right tail, which is nearly every money metric. The bigger the gap, the heavier the tail.

Worked, on ten orders:

£22  £24  £28  £31  £35  £38  £42  £48  £55  £2,400

mean     £272.30   ← no order was remotely near this
median    £36.50   ← the typical order

One trade customer makes the mean describe nothing. Reporting £272 as “average order value” is technically correct and practically a lie — and it’s the exact number that ends up in a shipping-threshold decision.

Which to use

Metric	Use	Why
Order value	Median, mean alongside	Heavy right tail
Revenue per visitor	Mean — but see below	You need the total, and the mean is what multiplies out
Time on page	Median or percentiles	Extreme right tail
Page load	p75	Convention, and the mean is meaningless — Percentiles in Performance
Conversion rate	Mean is the only option	It’s a proportion; there’s no median of 0s and 1s worth having

Revenue per visitor is the awkward case. You need the mean because revenue is additive — total revenue is mean × visitors, and the median doesn’t multiply out. So you’re stuck with the statistic most vulnerable to the tail, which is precisely why Winsorisation and Capping exists.

The reporting habit

Report the mean and the median together for any money metric. Two numbers, one line, and the gap between them tells the reader immediately whether the average is trustworthy.

average order value    £54.20
median order value     £38.00

Anyone reading that knows there’s a tail without being told. One number alone hides it.

Robustness

The property underneath all of this:

• The median is robust — change the largest value to £50,000 and it doesn’t move
• The mean is not — one value moves it arbitrarily far

That’s the entire argument for medians on skewed data, and the entire problem with them for anything you need to sum. See Outliers and Robust Statistics.

The mode

Rarely useful for continuous data, genuinely useful for categorical:

• Most common basket size, device, delivery option, entry page
• Bimodality is the real signal. Two modes almost always means two populations mixed — mobile and desktop, cached and uncached, consenting and not. That’s a segmentation finding — Segmentation (analysis)

Where it bites

• “Average customer” reasoning. Design decisions made for a customer whose profile is the mean of two distinct populations, and who therefore doesn’t exist
• Averages of averages. The mean of four category conversion rates isn’t the site rate unless the categories are equal size — Ratio Metrics
• Comparing means across periods where the tail changed. One large trade order can move a monthly mean enough to look like a trend — Skewed and Heavy-Tailed Distributions