Formularium Quantitative
methods
DD
Mean (x̄)
⨊ X/n
Median DD (n + 1) / 2
Range DD Largest – smallest value
DD
Sample Variance ( S2 )
DD
Standard deviation
√sample variance
DD A proportion of at least: 1 – 1 / k2
Eg. If K = 2 -> 1 – 1/22 = 0,75
Chebycheff So 75% of the observations will be within 2 standard
deviations of the sample mean
Lower Quartile DD (n+1) / 4
Upper quartile DD 3 x (n + 1) / 4
Inter quartile range DD Upper – lower quartile
Expected value of X P1
Long run average or mean of a discrete
random variable E(x) of 𝛍 = ⨊ x . P(x)
Expected value of X2 P1 E(x2) = ⨊ x2 . P(x)
P1 E(x2) – E(x)2 or 𝛍2
Variance random variable (𝛅2)
Standaardization property P1 / P2 Z=(x-𝛍)/𝛅
When n ≥30 then x̄ ∼N (𝛍 , 𝛅2 / n ) = APPROXIMATELY
When X ∼ N (𝛍, 𝛅2) then x̄ ∼N (𝛍 , 𝛅2 / n ) = EXACTLY
Standardization for samples S1
( < 30 )
S1
95 % confidence interval
methods
DD
Mean (x̄)
⨊ X/n
Median DD (n + 1) / 2
Range DD Largest – smallest value
DD
Sample Variance ( S2 )
DD
Standard deviation
√sample variance
DD A proportion of at least: 1 – 1 / k2
Eg. If K = 2 -> 1 – 1/22 = 0,75
Chebycheff So 75% of the observations will be within 2 standard
deviations of the sample mean
Lower Quartile DD (n+1) / 4
Upper quartile DD 3 x (n + 1) / 4
Inter quartile range DD Upper – lower quartile
Expected value of X P1
Long run average or mean of a discrete
random variable E(x) of 𝛍 = ⨊ x . P(x)
Expected value of X2 P1 E(x2) = ⨊ x2 . P(x)
P1 E(x2) – E(x)2 or 𝛍2
Variance random variable (𝛅2)
Standaardization property P1 / P2 Z=(x-𝛍)/𝛅
When n ≥30 then x̄ ∼N (𝛍 , 𝛅2 / n ) = APPROXIMATELY
When X ∼ N (𝛍, 𝛅2) then x̄ ∼N (𝛍 , 𝛅2 / n ) = EXACTLY
Standardization for samples S1
( < 30 )
S1
95 % confidence interval
