Lesson 3 — Averages & Medians

Finding average
ground

Two powerful ways to summarize data — and why neither tells the whole story.

Two types of data

◯ Continuous
  • Infinite values on a spectrum
  • Examples: height, weight, temperature
  • Can be 23.4, 10.5, 45.009…
■ Categorical
  • Distinct groups, no in-between
  • Examples: breed, blood type, species
  • No such thing as “half pug”

Definitions matter

Before measuring, you must agree on what you’re measuring. How tall is a dog?

❓ Tip of snout to tail? Sitting? Lying down?
✓ AKC standard: bottom of front paws to top of shoulder — no head!

NASA missions have failed over unit mix-ups (meters vs yards). Definitions save lives.

The Mean (average)

Sum all values, divide by how many. Represents the “typical” value.

Example — test scores: 85, 92, 78, 90, 88
85 + 92 + 78 + 90 + 88 = 433
433 ÷ 5 = 86.6

30 data points → 1 number. Much easier to reason about!

The Median

Sort all values, find the middle one. With an even count, average the two middle values.

12
15
18
21
22
25
28
30
→ Median = (21+22) ÷ 2 = 21.5

The median is less sensitive to extreme values than the mean.

When they disagree 🤰

Roseville: 999 people earn $60k/yr. One billionaire earns $2.3 billion/yr.

Mean income
$2,359,940
Skewed by the billionaire
Median income
$60,000
Reflects 99% of people

Outliers pull the mean away from the typical value. The median holds steady.

The bigger picture

Neither is the full story

Mean and median summarize the center of your data — but they hide how spread out the data is.

📈 Next up: variance and distributions — actually looking at the shape of your data.
1 / 7