📊 Descriptive Statistics, Probability Distributions
1️⃣ Descriptive Statistics with Pandas
Quick way to summarize datasets.
import pandas as pd
data = {"Marks": [85, 92, 78, 88, 90]}
df = pd.DataFrame(data)
print(df.describe()) # count, mean, std, min, max, etc.
print(df["Marks"].mean()) # Average
print(df["Marks"].median()) # Middle value
print(df["Marks"].mode()) # Most frequent value
2️⃣ Probability Basics
Chances of an event occurring (0 to 1)
Tossing a coin
prob_heads = 1 / 2
print(prob_heads) # 0.5
Multiple outcomes example:
from itertools import product
outcomes = list(product(["H", "T"], repeat=2))
print(outcomes) # [('H', 'H'), ('H', 'T'), ('T', 'H'), ('T', 'T')]
3️⃣ Normal Distribution using NumPy Seaborn
import numpy as np
import seaborn as sns
import matplotlib.pyplot as plt
data = np.random.normal(loc=0, scale=1, size=1000)
sns.histplot(data, kde=True)
plt.title("Normal Distribution")
plt.show()
4️⃣ Other Distributions
• Binomial → pass/fail outcomes
• Poisson → rare event frequency
• Uniform → all outcomes equally likely
Binomial Example:
from scipy.stats import binom
# 10 trials, p = 0.5
print(binom.pmf(k=5, n=10, p=0.5)) # Probability of 5 successes
🎯 Why This Matters
• Descriptive stats help understand data quickly
• Distributions help model real-world situations
• Probability supports prediction and risk analysis
Practice Task:
• Generate a normal distribution
• Calculate mean, median, std
• Plot binomial probability of success
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