FORMULARIO
I PARTE M=∑𝑥𝑖𝑛𝑖
𝑟
𝑖=1𝑛 𝑀𝑔=√∏𝑥𝑖
𝑛
𝑖=1
𝑛 𝑀𝑒=𝑥𝑠+𝑥𝑠−𝑥𝑠
𝐹(𝑥𝑠)−𝐹(𝑥𝑠−1)[0,50−𝐹(𝑥𝑠−1)]
K=x𝑚𝑎𝑥−𝑥𝑚𝑖𝑛 DI = x0,75 – x0,25 𝜎=√∑(𝑥𝑖−𝑀)2
𝑛
𝑖=1 𝑛= √𝑛−1
2𝑛 ∆2
𝜎𝑚𝑎𝑥=√(𝑀−𝑥𝑚𝑖𝑛)(𝑥𝑚𝑎𝑥− 𝑀) 𝑆𝑀=∑|𝑥𝑖−𝑀|
𝑛
𝑖=1𝑛 MAD = Me(|xi - Me|)
∆1=∆=∑ ∑ |𝑥𝑖−𝑥𝑗|
𝑛
𝑗=1
𝑛
𝑖=1𝑛(𝑛−1)= 2∑𝑥(𝑖)[2𝑖−(𝑛+1)]
𝑛
𝑖=1 𝑛(𝑛−1) ∆𝑚𝑎𝑥=2𝑛
𝑛−1 (𝑀−𝑥𝑚𝑖𝑛)(𝑥𝑚𝑎𝑥−𝑀)
𝑥𝑚𝑎𝑥−𝑥𝑚𝑖𝑛
∆2=√∑ ∑ |𝑥𝑖−𝑥𝑗|2
𝑛
𝑗=1
𝑛
𝑖=1𝑛(𝑛−1) 𝑉𝐴𝑅= ∑(𝑥𝑖−𝑀)2
𝑛
𝑖=1 𝑛= 𝑀22−𝑀2=𝜎2 𝑆𝑀𝑒=∑|𝑥𝑖−𝑀𝑒|
𝑛
𝑖=1 𝑛
𝑛𝛼=𝑛(𝑥𝑚𝑎𝑥−𝑀)
𝑥𝑚𝑎𝑥−𝑥𝑚𝑖𝑛 𝑛𝜔=𝑛−𝑛𝛼=𝑛(𝑀−𝑥𝑚𝑖𝑛
𝑥𝑚𝑎𝑥−𝑥𝑚𝑖𝑛
𝑅 =1 − 𝑛
𝑛−1(∑(𝑞𝑖′
𝑟
𝑖=1 +𝑞𝑖−1
′)𝑓𝑖−1
𝑛) 𝑅 = 𝑛+1
𝑛−1−2
𝑛−1∑𝑞𝑖′
𝑛
𝑖=1 𝑞𝑖=𝑥(𝑖)𝑛𝑖
∑𝑥𝑖𝑛𝑖
𝑟𝑖=1
𝑀=∑𝑥𝑖𝑤𝑖
𝑛
𝑖=1
∑𝑤𝑖
𝑛
𝑖=1 𝜎= √∑(𝑥𝑖−𝑀)2𝑤𝑖
𝑛
𝑖=1∑𝑤𝑖
𝑛
𝑖=1 𝑧𝑖=𝑥𝑖−𝑀
𝜎
𝐴𝑆1=𝑀−𝑀𝑒
𝜎 𝐴𝑆2=𝑀−𝑀𝑒
𝑠𝑀𝑒 𝐴𝑆3= √∑(𝑥𝑖−𝑀)3𝑓𝑖
𝑟
𝑖=1
3 𝐴𝑆4=(𝑥0,75−𝑀𝑒)−(𝑀𝑒−𝑥0,25)
𝛾(𝑋)=∑(𝑥𝑖−𝑀(𝑋))3𝑓𝑖
𝑟
𝑖=1[𝜎(𝑋)]3 ASr=(x0,75−Me)−(Me−x0,25)
x0,75− x0,25 𝐾𝑢=∑(𝑥𝑖−𝑀(𝑋))4𝑓𝑖
𝑟
𝑖=1 𝜎4
𝐶𝑂𝑉(𝑋,𝑌)=∑(𝑥𝑖−𝑀)(𝑦𝑖−𝑀)
𝑛
𝑖=1 𝑛 𝐺′=1−∑𝑓𝑖2
𝑝
𝑖=1
(𝑝−1)/𝑝 𝐻′=−∑𝑓𝑖𝑙𝑜𝑔𝑓𝑖
𝑝
𝑖=1
𝑙𝑜𝑔𝑝
a=∑𝑦𝑖 ∑𝑥𝑖2−∑𝑥𝑖∑𝑥𝑖𝑦𝑖
𝑛∑𝑥𝑖2−(∑𝑥𝑖)2=𝑀(𝑌)−𝑏𝑀(𝑋) b = 𝑛∑𝑥𝑖𝑦𝑖−∑𝑥𝑖∑𝑦𝑖
𝑛∑𝑥𝑖2−(∑𝑥𝑖)2=𝐶𝑂𝑉(𝑋,𝑌))
𝑉𝐴𝑅(𝑋) =𝑟𝑋𝑌σY
σX
𝑟𝑋𝑌=𝐶𝑂𝑉(𝑋,𝑌)
√𝑉𝐴𝑅(𝑋)𝑉𝐴𝑅(𝑌)=𝐶𝑂𝑉(𝑋,𝑌)
𝜎𝑋𝜎𝑌 𝑟𝑋𝑌
2=𝛿=𝐷𝐸𝑉(𝑌)
𝐷𝐸𝑉(𝑌)=1−𝐷𝐸𝑉(𝐸)
𝐷𝐸𝑉(𝑌)
Funzone esponenziale: f(t) = abt Funzione di potenza: f(t) = atb
per calcolatrice:
COV(X,Y) = rXY ·X ·Y DEV(Y) = (Y )2 · n DEV(ŷ)=r2 ·DEV(Y) DEV(E)=(1-r2 )·DEV(Y)
