📘 Chapter 6: Mathematical Functions and Statistics in NumPy — Crunch Numbers Like a Pro

🧠 “When it comes to numbers, NumPy doesn’t just play with them — it commands them.”

Welcome back to the sixth chapter of your NumPy learning journey! So far, we’ve learned how to create arrays, slice and dice them, and even perform powerful arithmetic operations using broadcasting.

But what’s the next logical step?

👉 Analysis.

Whether you’re working with small datasets or big data, you’ll often need to summarize, analyze, and draw insights. That’s where NumPy’s mathematical and statistical functions come into play.

In this chapter, you’ll learn:

• How to use NumPy’s built-in functions like sum(), mean(), std(), min(), max(), argmax(), and more.

• How to apply these functions along specific axes of multi-dimensional arrays.

• Real-life scenarios for using them effectively.

📊 1. The Need for Mathematical Functions

Whether you’re building machine learning models, performing data cleaning, or running simulations — you need to:

• Find averages

• Determine ranges and extremes

• Understand data variability

• Identify max/min positions

Instead of writing your own formulas, NumPy provides built-in, optimized functions — ready to use and blazing fast.

🧮 2. Basic Mathematical Functions

Let’s create an array to work with:

import numpy as np

arr = np.array([10, 20, 30, 40, 50])

🔹 np.sum() – Total sum

print("Sum:", np.sum(arr))  # 150

🔹 np.mean() – Average value

print("Mean:", np.mean(arr))  # 30.0

🔹 np.min() & np.max() – Extremes

print("Min:", np.min(arr))  # 10
print("Max:", np.max(arr))  # 50

🔹 np.std() – Standard deviation

print("Standard Deviation:", np.std(arr))  # Spread from the mean

🔹 np.var() – Variance

print("Variance:", np.var(arr))

🧠 3. Finding Indices of Extremes

🔹 np.argmax() – Index of the largest value

print("Index of Max:", np.argmax(arr))  # 4

🔹 np.argmin() – Index of the smallest value

print("Index of Min:", np.argmin(arr))  # 0

🧊 4. Axis-Based Computations

When working with 2D or higher arrays, you can specify the axis along which to perform operations.

Let’s create a matrix:

matrix = np.array([
    [1, 2, 3],
    [4, 5, 6]
])

🟦 Axis 0 = Column-wise (downward)

🟥 Axis 1 = Row-wise (across)

🔸 Sum by rows

print("Row-wise Sum:", np.sum(matrix, axis=1))  # [6 15]

🔸 Sum by columns

print("Column-wise Sum:", np.sum(matrix, axis=0))  # [5 7 9]

🔸 Mean by rows

print("Row-wise Mean:", np.mean(matrix, axis=1))

🔸 Max per column

print("Max per column:", np.max(matrix, axis=0))  # [4 5 6]

🧩 5. Other Useful Mathematical Functions

🔹 np.cumsum() – Cumulative sum

arr = np.array([1, 2, 3, 4])
print("Cumulative Sum:", np.cumsum(arr))  # [1 3 6 10]

🔹 np.cumprod() – Cumulative product

print("Cumulative Product:", np.cumprod(arr))  # [1 2 6 24]

🔹 np.percentile() – Statistical percentiles

arr = np.array([1, 3, 5, 7, 9])
print("50th Percentile (Median):", np.percentile(arr, 50))  # 5

🔹 np.median() – Middle value

print("Median:", np.median(arr))  # 5

🧪 6. Real-Life Applications

🧰 Bonus: Normalization with NumPy

Zero-centering an array (subtract the mean)

arr = np.array([10, 20, 30])
normalized = arr - np.mean(arr)
print(normalized)  # [-10.  0.  10.]

Scaling to 0–1 range (Min-Max Normalization)

scaled = (arr - np.min(arr)) / (np.max(arr) - np.min(arr))
print(scaled)  # [0.  0.5 1.]

⚠️ 7. Common Mistakes to Avoid

🧾 Summary Table: NumPy Math & Stats

🔚 Wrapping Up Chapter 6

Congratulations! 🎉
You now have the tools to extract deep insights from any dataset using NumPy’s statistical arsenal. Whether it’s finding an average, spotting an outlier, or identifying the max performer — NumPy makes it effortless.

These are essential skills for:

• Data science

• AI/ML

• Financial modeling

• Scientific computing

• Signal/image analysis

🔜 Coming Next in Chapter 7:

We’ll cover:

• Linear Algebra with NumPy — dot product, matrix multiplication, transpose, inverse, and more.