# Mean, Median and Mode

> The mean, median and mode measure the centre of data in different ways. Learn when each is best for trading data, how outliers distort averages and geometric means.

Source: https://learn.tradelabsai.com/math/mean-median-and-mode/  
Track: Math and Statistics · Level: Intermediate · Updated: 2026-10-03  
Publisher: TradeLabs AI (https://tradelabsai.com). Education, not financial advice.  
Cite as: TradeLabs Learn, "Mean, Median and Mode", https://learn.tradelabsai.com/math/mean-median-and-mode/

An average is supposed to describe a typical value, but there are several kinds, and they can tell very different stories. The mean adds everything up and divides; the median picks the middle value; the mode is the most common value. In trading, where results are often skewed by a few big wins or losses, choosing the wrong average can make a strategy look much better or worse than it really is. Returns over time also need a special average, the geometric mean.

## The three main averages

| Measure | How to calculate | Strength | Weakness |
|---|---|---|---|
| Mean (arithmetic) | Sum of values divided by count | Uses all data; key for expected value | Pulled by outliers |
| Median | Middle value when sorted | Robust to outliers | Ignores the size of extremes |
| Mode | Most frequent value | Useful for categories and discrete data | May not exist or be unique |

## Worked example

**Example: Ten trades**
Profits on ten trades, in dollars: minus 50, minus 40, minus 40, minus 30, minus 20, 10, 20, 30, 40, 900.

- **Mean:** (minus 180 + 1,000) / 10 = 820 / 10 = $82.
- **Median:** the middle two values are minus 20 and 10, so the median is minus $5.
- **Mode:** minus $40 (appears twice).

The mean says the typical trade makes $82; the median says the typical trade loses $5. One $900 winner drives the mean. Both are true, and both matter: the strategy's profitability depends on that rare big win. See [Outliers and Robust Statistics](https://learn.tradelabsai.com/math/outliers-and-robust-statistics/).

## Mean vs median in skewed data

| Data shape | Relationship |
|---|---|
| Symmetric | Mean ≈ median |
| Right skewed (a few large positive values) | Mean > median |
| Left skewed (a few large negative values) | Mean < median |

Trend following and option buying often produce right skewed results: many small losses and a few large wins. Option selling and many mean reversion strategies often produce left skewed results: many small wins and occasional large losses. See [Skewness and Kurtosis](https://learn.tradelabsai.com/math/skewness-and-kurtosis/).

## Arithmetic vs geometric mean for returns

For returns that compound over time, the arithmetic mean overstates what you actually earn. The geometric mean gives the true average growth rate.

```
arithmetic mean = (r1 + r2 + ... + rn) / n
geometric mean = [(1 + r1) × (1 + r2) × ... × (1 + rn)]^(1/n) - 1
```

**Example: Up 50%, down 50%**
An investment gains 50% in year one and loses 50% in year two. Arithmetic mean: (50% minus 50%) / 2 = 0%. But $100 becomes $150, then $75: a 25% loss. Geometric mean: (1.5 × 0.5)^(1/2) minus 1 = √0.75 minus 1 ≈ minus 13.4% a year. The geometric mean matches what actually happened. See [Compounding and Geometric vs Arithmetic Returns](https://learn.tradelabsai.com/math/compounding/) and [Measuring Returns and CAGR](https://learn.tradelabsai.com/portfolio/measuring-returns-and-cagr/).

A useful approximation: geometric mean ≈ arithmetic mean minus half the variance. Higher volatility lowers compound returns, a drag sometimes called volatility drag.

## Weighted averages

Sometimes values deserve different weights, such as portfolio returns weighted by position size, or VWAP, which weights prices by volume. See [VWAP](https://learn.tradelabsai.com/volume/vwap/).

```
weighted mean = Σ (weight × value) / Σ weights
```

## Which average to use

| Question | Best measure |
|---|---|
| Average profit per trade for expected value | Mean |
| Typical trade experience | Median |
| Most common outcome | Mode |
| Long run growth rate of returns | Geometric mean |
| Average price paid across trades of different size | Weighted mean |

## Averages in your journal

When reviewing trades, report the mean, the median and the share of total profit coming from your best few trades. If removing the top three trades turns a profitable year into a losing one, your results depend on rare outliers, which is fine for some strategies but should be expected and planned for. See [Trading Journal](https://learn.tradelabsai.com/start-here/trading-journal/).

## Frequently asked questions

### What is the difference between mean and median?

The mean is the sum divided by the count and is affected by outliers; the median is the middle value and is resistant to outliers.

### Why use the geometric mean for returns?

Because returns compound, and the geometric mean shows the actual average growth rate, while the arithmetic mean overstates it when returns vary.

### Which average should I use for trading results?

Use the mean for expected value, the median to see a typical trade, and the geometric mean to measure compound growth.

Next, learn how spread is measured in [Variance and Standard Deviation](https://learn.tradelabsai.com/math/variance-and-standard-deviation/).

## Continue learning

- Next lesson: [Variance and Standard Deviation](https://learn.tradelabsai.com/math/variance-and-standard-deviation/)
- Previous lesson: [Random Variables](https://learn.tradelabsai.com/math/random-variables/)
- Related: [Random Variables](https://learn.tradelabsai.com/math/random-variables/): A random variable assigns numbers to uncertain outcomes, like a trade's profit. Learn discrete and continuous variables, expectation and variance, with examples.
- Related: [Variance and Standard Deviation](https://learn.tradelabsai.com/math/variance-and-standard-deviation/): Variance and standard deviation measure how spread out values are. Learn the formulas, sample vs population, annualising volatility and their role in trading risk.
- Related: [Outliers and Robust Statistics](https://learn.tradelabsai.com/math/outliers-and-robust-statistics/): Outliers can distort averages, correlations and backtests. Learn how to detect them, robust measures like the median and MAD, winsorising and when they matter.
- Related: [Skewness and Kurtosis](https://learn.tradelabsai.com/math/skewness-and-kurtosis/): Skewness measures whether returns lean to one side; kurtosis measures tail heaviness. Learn the formulas, what they reveal about strategies and how to use them.
- Related: [Compounding and Geometric vs Arithmetic Returns](https://learn.tradelabsai.com/math/compounding/): Compounding means returns earn returns over time. Learn the formulas, why losses hurt more than gains help, volatility drag and how it shapes position sizing.
- Related: [Measuring Returns and CAGR](https://learn.tradelabsai.com/portfolio/measuring-returns-and-cagr/): Learn how to measure trading and investment returns correctly: simple and log returns, CAGR, arithmetic versus geometric averages, and money weighted returns.