Variance

𝜎²

𝜎̂²or 𝑠²

• measures how far a set of numbers are spread out from their average value
• calculation of variance uses squares because it weights outliers more heavily than data very near the mean. This calculation also prevents differences above the mean from canceling out those below, which can sometimes result in a variance of zero

Standard Deviation

𝜎

𝜎̂ or 𝑠

• measures how far a set of numbers are spread out from their average value
• brings variance back to the original unit of data

p-Quantiles

𝑞_𝑝

𝑞̂_𝑝

• generalizes median from 0.5 to a range [0,1]
• quantiles are cut points dividing the range of a probability distribution into continuous intervals with equal probabilities
• variants: median, quartiles, percentile, etc

Coefficient of Variation

• TODO

Max
Min

• For a subset 𝑆 of field 𝐹, 𝑠̃∊𝑆 is called the max of 𝑆 if: ∀𝑠∊𝑆: 𝑠≤𝑠̃
• For a subset 𝑆 of field 𝐹, 𝑠̃∊𝑆 is called the min of 𝑆 if: ∀𝑠∊𝑆: 𝑠≥𝑠̃

Upper Bound
Lower Bound

• For a subset 𝑆 of field 𝐹, 𝑠̃∊𝐹 is called an upper bound of 𝑆 if: ∀𝑠∊𝑆: 𝑠≤𝑠̃
• For a subset 𝑆 of field 𝐹, 𝑠̃∊𝐹 is called a lower bound of 𝑆 if: ∀𝑠∊𝑆: 𝑠≥𝑠̃

Supremum
Infimum

• For a subset 𝑆 of field 𝐹, 𝑠̃∊𝐹 is called the supremum of 𝑆 if:
  • 𝑠̃ is an upper bound of 𝑆
  • 𝑠̃≤𝑠 for any other upper bound 𝑠∊𝑆
• For a subset 𝑆 of field 𝐹, 𝑠̃∊𝐹 is called the infimum of 𝑆 if:
  • 𝑠̃ is a lower bound of 𝑆
  • 𝑠̃≥𝑠 for any other lower bound 𝑠∊𝑆

Range

• range = max - min

Mode Deviation

• is the most occurring distance between each data point and the mean

Median Deviation

• is the middle distance between each data point and the mean

Variation

• is the variance of the distances between each data point