O‘zgaruvchanlik
Tavsifiy statistika tendensiya va o‘zgaruvchanlikka bo‘linadi.
O‘zgaruvchanlik quyidagi ko‘rsatkichlardan foydalanadi:
- Minimum va maksimum
- Dispersiya
- Chetlanish
- Taqsimot
- Asimmetriya (skewness)
- Ekstsess (kurtosis)
Dispersiya
Statistikada dispersiya — qiymatlarning o‘rtacha qiymatdan farqlari kvadratlarining o‘rtachasi.
Boshqacha aytganda, dispersiya sonlar to‘plami o‘rtacha qiymatdan qanchalik tarqalganini tavsiflaydi.
O‘rtacha qiymat oldingi bobda tushuntirilgan.
Ushbu jadvalda 11 ta qiymat bor:
| 7 | 8 | 8 | 9 | 9 | 9 | 10 | 11 | 14 | 14 | 15 |
Dispersiyani hisoblang:
// Calculate the Mean (m)
let m = (7+8+8+9+9+9+10+11+14+14+15)/11;
// Calculate the Sum of Squares (ss)
let ss = (7-m)**2 + (8-m)**2 + (8-m)**2 + (9-m)**2 + (9-m)**2 + (9-m)**2 + (9-m)**2 + (10-m)**2 + (11-m)**2 + (14-m)**2 + (15-m)**2;
// Calculate the Variance
let variance = ss / 11;
Yoki math.js kabi matematik kutubxonadan foydalaning:
const values = [7,8,8,9,9,9,10,11,14,14,15];
let variance = math.variance(values, "uncorrected");
Standart chetlanish
Standart chetlanish — sonlar qanchalik tarqoq ekanining o‘lchovi.
Uning belgisi — σ (yunoncha sigma harfi).
Formulasi — √ dispersiya (dispersiyadan olingan kvadrat ildiz).
Standart chetlanish (JavaScript’da):
// Calculate the Mean (m)
let m = (7+8+8+9+9+9+10+11+14+15)/11;
// Calculate the Sum of Squares (ss)
let ss = (7-m)**2 + (8-m)**2 + (8-m)**2 + (9-m)**2 + (9-m)**2 + (9-m)**2 + (9-m)**2 + (10-m)**2 + (11-m)**2 + (14-m)**2 + (15-m)**2;
// Calculate the Variance
let variance = ss / 11;
// Calculate the Standard Deviation
let std = Math.sqrt(variance);
Chetlanish — masofa o‘lchovi.
Barcha qiymatlar o‘rtacha qiymatdan (markazdan) o‘rtacha hisobda qanchalik uzoqda ekani.
Yoki math.js kabi matematik kutubxonadan foydalansangiz:
const values = [7,8,8,9,9,9,9,10,11,14,15];
let std = math.std(values, "uncorrected");
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