compare() — Mean vs median vs mode

How the three averages are computed — and which to reach for.

compare(mean, median, mode)

Key idea

• Mean: add all values and divide by the count; uses every value but is dragged by outliers (extreme values). (e.g. (2+4+6)/3 = 4)
• Median: sort and take the middle value; ignores how extreme outliers are, so it stays steady. (e.g. middle of 1, 3, 100 = 3)
• Mode: the most frequent value; the only average that works on categories. (e.g. 2,2,5,7,7,7 -> 7)
• On data that leans right (a long high tail) they separate: mode < median < mean. (e.g. mode 35 < median 36 < mean 48)

Which average should you use?

1. Use the MEAN when the data is roughly symmetric with no wild outliers — average height, average test score, average temperature.
2. Use the MEDIAN when the data is skewed or has outliers — incomes, house prices, waiting times — because it shrugs off the extremes.
3. Use the MODE for categories or to name the most common choice — favourite colour, most-sold shoe size, busiest hour.

Definition

$$\text{mean}=\frac{\sum x_i}{n}\text{median}=\text{middle of sorted}\text{mode}=\text{most frequent}$$

$\sum x_i$

add up all the values

$n$

how many values

$\text{median}$

the middle once sorted

$\text{mode}$

the value that repeats most

In plain words

Three ways to say "typical": add-and-share (mean), the one in the middle (median), and the one you see most (mode). Pick by how lopsided your data is and whether it’s numbers or labels.

Where you'd use it

• A salary table with a few huge earners: the median tells the typical pay, while the mean is inflated by the top few.
• A survey of favourite ice-cream flavours: only the mode makes sense — you cannot average a flavour.
• Exam scores that are fairly symmetric: the mean is the natural summary, and it nearly matches the median.

Frequently asked questions

What does the gap between mean and median tell me?

The skew direction: mean > median usually means right (positive) skew.