Data & the Normal Curve
Real data has a shape. Build a data set, watch the mean, median and spread react as you drag it around, and see when it settles into the famous bell where the 68–95–99.7 rule takes over. Grade 11–12.
Where's the middle? How spread out?
Two questions describe almost any data set. First, the centre: the mean (the balance point — add everything, divide by how many), the median (the middle value in order), and the mode (the most common). Second, the spread: the range (highest − lowest) and the standard deviation σ, the typical distance of a value from the mean.
Drag the data 🔴
Drag the dots along the axis. Pull one far out to make an outlier — watch the orange mean chase it while the green median barely flinches. Switch on the normal curve and the 68–95–99.7 rule.
Mean vs. median — who moves?
The mean is sensitive
Every value tugs on the mean, so a single extreme point drags it a long way. Great for balanced data, misleading when there's an outlier.
The median is stubborn
The median only cares about the middle of the order, not how far the extremes reach — so it barely moves. That's why "median income" beats "mean income".
The bell and the 68–95–99.7 rule
Pile up enough natural measurements — heights, test scores, errors — and they fall into the normal distribution, the symmetric bell centred on the mean. Its magic is the empirical rule: about 68% of the data sits within one σ of the mean, 95% within two, and 99.7% within three. Turn on the rule and compare the ideal percentages to your own data.