Lesson 4 — Variance & Distributions
Why the mean alone can fool you — and how spread, shape, and histograms tell the full story.
A concert seller advertises an average ticket price of $20. But best seats are $100, worst are $5 — the mean hides the spread!
How much do data points differ from the mean? Variance measures the average squared distance from the mean.
Example: heights [2,4,6,8,10] → mean=6 → variance = 10
The square root of variance. Easier to interpret: the “typical distance” a value sits from the mean.
Rhonda at 30″ is 3 SD above the mean — only 0.1% of dogs are that tall!
Many real-world variables follow a bell-shaped curve. Most values cluster near the mean; fewer appear at the extremes.
Height, test scores, plant growth — all tend to follow a normal distribution.
Data can be skewed or have multiple peaks. Shape matters for choosing the right test.
Visualization tool
Bars show how many data points fall in each range. Histograms reveal the shape of your data — symmetric, skewed, bimodal — at a glance.
The McDonald’s Times Square example: Thursday traffic has two peaks (lunch + dinner), Saturday’s is closer to normal. Same data, very different shapes!