Representation and summary of data
Stem-and-leaf diagrams and box plots
Two ways to see a whole data set at a glance. A stem-and-leaf diagram keeps every value; a box plot squeezes the data into five numbers that show its centre, its spread and its shape.
≈ 30 minHistograms and cumulative frequency
In a histogram, area (not height) shows frequency, which is what makes unequal class widths fair. A cumulative frequency graph turns the same table into a curve from which the median and quartiles can be read.
≈ 35 minMean and standard deviation
The mean is the balance point of the data; the standard deviation is a typical distance from it. One formula, "mean of the squares minus the square of the mean", gives the variance from almost any form of data.
≈ 35 minCoded and combined data
Shifting every value moves the mean but leaves the spread alone; scaling every value scales both. Knowing this, you can work with simpler "coded" numbers and translate back, and you can merge two groups using their totals.
≈ 30 min