Statistiques avec un tableur et en Python

=MOYENNE(A2:A11)                         → 22,3
=MOYENNE(B2:B11)                         → 33,4
=PENTE(B2:B11;A2:A11)                    → 1,2357…
=ORDONNEE.ORIGINE(B2:B11;A2:A11)         → 5,8435…
=COEFFICIENT.CORRELATION(A2:A11;B2:B11)  → 0,9987…
=PREVISION.LINEAIRE(30;B2:B11;A2:A11)    → 42,9…

import statistics as st

# Durées des 17 interventions de la base parc (en minutes)
durees = [45, 20, 30, 40, 10, 60, 90, 120, 15, 15, 240, 180, 150, 55, 35, 90, 60]

print("Effectif     :", len(durees))
print("Moyenne      :", round(st.mean(durees), 2))
print("Médiane      :", st.median(durees))
print("Modes        :", st.multimode(durees))
print("Écart type σ :", round(st.pstdev(durees), 2))   # divise par N
print("Écart type s :", round(st.stdev(durees), 2))    # divise par N - 1
print("Quartiles    :", st.quantiles(durees, n=4, method="inclusive"))
print("Étendue      :", max(durees) - min(durees))

Effectif     : 17
Moyenne      : 73.82
Médiane      : 55
Modes        : [60, 90, 15]
Écart type σ : 62.95
Écart type s : 64.89
Quartiles    : [30.0, 55.0, 90.0]
Étendue      : 230

import statistics as st

sessions = [4, 8, 12, 15, 20, 24, 28, 33, 37, 42]
cpu = [11, 15, 22, 24, 31, 34, 41, 46, 52, 58]

pente, ordonnee = st.linear_regression(sessions, cpu)
r = st.correlation(sessions, cpu)

print(f"y = {pente:.2f}x + {ordonnee:.2f}")
print(f"r = {r:.4f}  r² = {r * r:.4f}")
print("Point moyen :", st.mean(sessions), st.mean(cpu))
print(f"Prévision pour 30 sessions : {pente * 30 + ordonnee:.1f} %")

y = 1.24x + 5.84
r = 0.9987  r² = 0.9974
Point moyen : 22.3 33.4
Prévision pour 30 sessions : 42.9 %

import statistics as st


def somme_carres(x, y, a, b):
    """Somme des carrés des écarts entre les y observés et la droite y = ax + b."""
    return sum((yi - (a * xi + b)) ** 2 for xi, yi in zip(x, y))


volume = [20, 40, 60, 80, 100]     # Go
duree = [14, 22, 33, 41, 50]       # min

a, b = st.linear_regression(volume, duree)
print(f"Droite des moindres carrés : y = {a:.3f}x + {b:.1f}")
for pente, ordonnee in [(a, b), (0.45, 5), (0.46, 4.4), (0.5, 2)]:
    print(f"a = {pente:.3f}, b = {ordonnee:.1f} -> S = {somme_carres(volume, duree, pente, ordonnee):.2f}")

Droite des moindres carrés : y = 0.455x + 4.7
a = 0.455, b = 4.7 -> S = 1.90
a = 0.450, b = 5.0 -> S = 2.00
a = 0.460, b = 4.4 -> S = 2.00
a = 0.500, b = 2.0 -> S = 10.00

import math
import statistics as st

mois = [1, 2, 3, 4, 5, 6, 7, 8]
volume = [10.0, 11.3, 12.5, 14.1, 15.8, 17.6, 19.8, 22.2]   # Go

z = [math.log(v) for v in volume]                  # changement de variable z = ln y
a, b = st.linear_regression(mois, z)               # ajustement affine de z en x
k, q = math.exp(b), math.exp(a)                    # retour à y = k × q^x

print(f"z = {a:.3f}x + {b:.3f}")
print(f"y = {k:.1f} × {q:.2f}^x")
print(f"r(x, y) = {st.correlation(mois, volume):.4f}")
print(f"r(x, z) = {st.correlation(mois, z):.4f}")
seuil = (math.log(48) - b) / a
print(f"48 Go atteints pendant le mois n° {math.ceil(seuil)}")

z = 0.113x + 2.191
y = 8.9 × 1.12^x
r(x, y) = 0.9933
r(x, z) = 0.9999
48 Go atteints pendant le mois n° 15

import csv
import io
import statistics as st

# Extrait d'un export CSV de Zabbix : horodatage et temps de réponse (en secondes)
export = """clock;value
2026-11-02 09:00;0.212
2026-11-02 09:05;0.198
2026-11-02 09:10;0.231
2026-11-02 09:15;0.187
2026-11-02 09:20;0.640
2026-11-02 09:25;0.205
2026-11-02 09:30;0.219
2026-11-02 09:35;0.193
"""

lecteur = csv.DictReader(io.StringIO(export), delimiter=";")
temps_ms = [float(ligne["value"]) * 1000 for ligne in lecteur]

print("Mesures  :", len(temps_ms))
print(f"Moyenne  : {st.mean(temps_ms):.1f} ms")
print(f"Médiane  : {st.median(temps_ms):.1f} ms")
print(f"σ        : {st.pstdev(temps_ms):.1f} ms")
print(f"Maximum  : {max(temps_ms):.1f} ms")

Mesures  : 8
Moyenne  : 260.6 ms
Médiane  : 208.5 ms
σ        : 144.0 ms
Maximum  : 640.0 ms

SELECT COUNT(*)                        AS n,
       ROUND(AVG(duree_min), 1)        AS moyenne,
       ROUND(STDDEV_POP(duree_min), 1) AS ecart_type,
       MIN(duree_min)                  AS mini,
       MAX(duree_min)                  AS maxi
FROM intervention;

SELECT e.prenom, e.nom,
       COUNT(*)                          AS n,
       ROUND(AVG(i.duree_min), 1)        AS moyenne,
       ROUND(STDDEV_POP(i.duree_min), 1) AS ecart_type
FROM intervention i
JOIN employe e ON e.id_employe = i.id_technicien
GROUP BY e.id_employe, e.prenom, e.nom
ORDER BY moyenne;