Unit 16
Statistics.
Many measurements in a few numbers: averages, spread, histograms, the bell curve, correlation and the line of best fit.
Before this unit
The unit, lesson by lesson
Lessons
5 lessons · 27 practice questions · about 2 hours
Mean, median and mode
Three ways to give a long list of readings one number: the balance point, the value in the middle and the most common value, and what happens to each when a bad reading creeps in.
Range and standard deviation
Two groups with the same mean can be very different. How far the values spread: the range, the standard deviation and why it squares, and what share of the readings falls within one standard deviation.
The normal distribution
A histogram shows how data spread out. On a Galton board: the mode is the tallest bar, the standard deviation grows like the square root of the number of rows, and the $68$–$95$ rule: how much of the data lies within one and two standard deviations.
Correlation
Two variables together: the scatter plot, the direction and strength of a link, the correlation coefficient $r$ and what it does not measure: not the slope, not a link that is not a straight line, and not a cause.
The line of best fit
Which straight line fits a cloud of points best? Turn a line by hand until the squares add up to the least, and discover least squares, the balance point, predicting from the line, and what an outlier does to it.