📊 Data
✨Scatter Plots & Correlation
Plot two quantities on one grid and the shape of the point cloud tells you how they move together.
A bar graph answers one quantity at a time, but in real life quantities often travel in pairs: the hotter the day, the more ice cream sells; the longer you run, the more energy you burn. To see how two quantities change together, plot them on the same grid — a scatter plot.
One point, two quantities
In Cartesian coordinates a point is written — which is exactly two numbers! A scatter plot exploits this: one quantity on the horizontal axis, the other on the vertical, and every data pair drops in as one point. Record the daily temperature and ice cream sales for a week and you get seven points. A bar graph compares bars one by one; a scatter plot is read through the shape of the whole cloud.
Three kinds of correlation
The cloud takes roughly three shapes:
- Positive correlation: points climb from bottom-left to top-right — when one grows, so does the other, like height and arm span;
- Negative correlation: points slide from top-left to bottom-right — when one grows, the other shrinks, like temperature and coat sales;
- No correlation: points scattered everywhere with no direction, like shoe size and math scores.
(3, -2) → Quadrant IV
Walk x steps horizontally, then y steps vertically — the ordered pair (x, y) pins down exactly one point.
Place a few points on the plotting board: lined up as a rising slope is positive correlation, a falling slope is negative, and a random scatter is none at all.
Lines of best fit and outliers
If the points form a loose band, you can draw a straight line by eye through the middle of them, keeping the points evenly spread on both sides — a line of best fit. It sums up how the quantities move together overall. A point far away from the crowd is an outlier: maybe a copied-down number, maybe a genuinely special case — always give it a second look before drawing your line.
Correlation is not causation
Does ice cream cause drowning?
Statistics show that in months when ice cream sells more, more people drown. Is ice cream dangerous? No — the real cause is hot weather: hot days push both numbers up at once. Ice cream and drowning are just partners in the same trend; neither causes the other.
Correlation says "the two quantities move together", not "one causes the other". Whenever you meet a strong correlation, ask: is there a third quantity pushing both of them from behind?
Check yourself
Quick quiz
1. Points in a scatter plot run from bottom-left to top-right. What kind of correlation is this?
2. Ice cream sales and drownings rise and fall together. What is the best explanation?
3. What do you call a point far away from all the others in a scatter plot?