Bin mean, bin median, bin boundary
sort, cut into bins of equal count, then replace every value by the bin's mean, or its median, or its nearer extreme
Whenever a question says 'smooth by binning' or gives a bin size. Bins hold an equal count, not an equal width. Ties on the boundary rule are broken downwards in the class's worked slides.
- bin size
- Number of values per bin, given in the question
- bin mean
- Average of the values in that bin; replaces all of them
- bin median
- Middle value, or the average of the two middle values for an even count
- bin boundary
- The bin's smallest and largest values; interior values move to whichever is nearer
Min-max normalisation
x' = (x - min) / (max - min) maps into [0, 1]
When several series of different magnitudes must share one axis, or when a visual encoding needs a bounded input such as colour intensity or marker size. Sensitive to the extremes, so one new record can rescale everything.
- x
- The original value
- min, max
- Smallest and largest values in that column
- x'
- The normalised value; the minimum becomes 0 and the maximum becomes 1
Standardisation (z-score)
z = (x - mean) / SD gives mean 0 and SD 1
When the question is whether several series move together, or when outliers make a min-max range unrepresentative. Produces negative values, so it cannot feed a visual that needs non-negative numbers.
- x
- The original value
- mean
- Average of the column
- SD
- Standard deviation of the column
- z
- How many standard deviations above (positive) or below (negative) the mean the value lies