Level 6: Two variables

Statistics and data · level 6 of 8 · rough age 13-14 (a guide for parents; anyone can start anywhere)

Until now every data set has been one list of numbers. In this level each person or thing gives you two numbers, such as hours studied and test score, and the question becomes: do they move together? You draw scatter plots, describe correlation in words, fit a straight line by eye and use it to predict, and learn when a prediction is safe and when it is nonsense. You also meet the most important warning in statistics, that correlation is not causation. The level ends with the standard deviation, the measure of spread that the rest of statistics is built on.

Lesson	You will be able to
Scatter plots	Plot pairs of data, choose which variable goes on which axis, and read a scatter plot
Correlation	Describe a pattern as positive, negative or none, strong or weak, straight or curved, in clear words
Line of best fit by eye	Draw a balanced line through a scatter plot, find its equation from two points, and predict with it
Interpolation and extrapolation	Tell a prediction inside the data from one outside it, and explain why going far outside is risky
Correlation is not causation	Spot lurking variables, reverse cause and coincidence, and say what kind of study can show cause
Standard deviation	Calculate the standard deviation by hand and with technology, and explain each step and the n − 1 version

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