Math & Statistics for Data Science: Core Foundations

Understand the role of Math & Statistics for Data Science in the data-science workflow

A churn model can be explained mathematically as a sequence: standardize numerical variables, multiply feature values by learned weights, transform the score into a probability, then compare predictions with observed outcomes.

• The useful part of the topic is not the label but the behavior it explains.
• Statistics helps summarize data and reason about uncertainty; probability gives a language for uncertain outcomes; linear algebra represents data compactly; calculus explains how optimization changes model parameters.
• A good check is to reproduce the idea on a tiny dataset before scaling it to a notebook or dashboard.
• You do not need to become a pure mathematician before building models.

Connect the idea to a concrete decision

For Math & Statistics for Data Science, predict one visible result before each snippet runs—a row count, shape, statistic, ranking or error pattern—then compare it with the printed checkpoint.

# Math & Statistics for Data Science · example 1
import numpy as np
x = np.array([2.0, 4.0, 6.0])
print('mean =', x.mean())
print('variance =', x.var(ddof=1))
print('norm =', np.linalg.norm(x))

Math & Statistics for Data Science checkpoint 1: Run the cell and inspect the printed values before changing anything.

# Math & Statistics for Data Science · example 2
import pandas as pd

df = pd.read_csv('practice.csv')
print(df.shape)
print(df.dtypes)
print(df.head(3).to_string(index=False))

Math & Statistics for Data Science checkpoint 2: (30, 5)
Column types are printed, followed by the first three rows.

# Math & Statistics for Data Science · example 3
missing = df.isna().sum().sort_values(ascending=False)
print(missing[missing.gt(0)])

Math & Statistics for Data Science checkpoint 3: Only columns with at least one missing value are listed.

# Math & Statistics for Data Science · example 4
summary = df.select_dtypes('number').agg(['count','mean','median','min','max']).T
print(summary.round(2))

Math & Statistics for Data Science checkpoint 4: A compact numeric summary appears with one row per numeric column.

# Math & Statistics for Data Science · example 5
test = df.copy()
if len(test):
    test.iloc[0, 0] = test.iloc[0, 0]
print('rows:', len(test), 'duplicates:', test.duplicated().sum())

Math & Statistics for Data Science checkpoint 5: The row count and duplicate count make the check visible instead of implicit.

Use a small reproducible example

Self-check with answers

Check your understanding with a changed input