Basic Statistics with NumPy

Before you can build any ML model, you need to understand your data. Statistics helps you answer simple questions like: What is the average? What is the highest value? How spread out is the data?

NumPy gives you ready-made functions for all of these.

---

1. Mean (Average)

The mean is the average of all numbers. Add them all up and divide by how many there are.

import numpy as np

marks = np.array([85, 90, 78, 92, 88])

average = np.mean(marks)
print("Mean:", average)  # Output: Mean: 86.6

In ML: The mean of your data tells you the "center" — what a typical value looks like.

---

2. Median (Middle Value)

The median is the middle number when you sort the data. It is more useful than mean when your data has extreme values (outliers).

import numpy as np

salaries = np.array([30000, 35000, 32000, 28000, 500000])

print("Mean:", np.mean(salaries))    # Output: Mean: 125000.0  (misleading!)
print("Median:", np.median(salaries))  # Output: Median: 32000.0  (more accurate!)

Why median matters: If one person earns ₹5 lakhs and others earn ₹30K, the mean gets pulled up. The median gives a better picture of what most people earn.

---

3. Min, Max, and Sum

import numpy as np

scores = np.array([72, 85, 91, 68, 95])

print("Min:", np.min(scores))   # Output: Min: 68
print("Max:", np.max(scores))   # Output: Max: 95
print("Sum:", np.sum(scores))   # Output: Sum: 411

---

4. Standard Deviation (How Spread Out is the Data?)

Standard deviation tells you how far the numbers are from the mean. A small number means the data is tightly packed. A big number means the data is spread out.

import numpy as np

# Consistent student: marks are close together
student_a = np.array([80, 82, 78, 81, 79])
print("Std Dev (A):", np.std(student_a))  # Output: ~1.41

# Inconsistent student: marks jump around
student_b = np.array([50, 95, 60, 90, 55])
print("Std Dev (B):", np.std(student_b))  # Output: ~18.17

In ML: Standard deviation helps you see if your data needs scaling before feeding it to a model. If one feature has values from 1-10 and another has 1000-50000, the model gets confused. We fix this using feature scaling.

---

5. What is a Vector? (Intuition for ML)

In everyday language, a vector is just a list of numbers.

import numpy as np

# This is a vector (1D array)
student_features = np.array([85, 72, 3.8])
# Meaning: [marks, attendance%, GPA]

In ML, each data point (like a student) is stored as a vector of features. The ML model learns patterns from these vectors.

---

6. What is a Matrix? (Intuition for ML)

A matrix is a table of numbers — many vectors stacked together.

import numpy as np

# Each row = one student
# Columns = [marks, attendance%, GPA]
student_data = np.array([
    [85, 72, 3.8],
    [90, 95, 3.9],
    [60, 50, 2.5],
    [78, 88, 3.2]
])

print("Shape:", student_data.shape)  # Output: (4, 3) → 4 students, 3 features

# Get the average marks (first column)
avg_marks = np.mean(student_data[:, 0])
print("Average marks:", avg_marks)  # Output: 78.25

In ML terminology:

• Each row is a sample (one data point)
• Each column is a feature (one measurement)
• The entire table is your dataset

---

Summary

Function	What it Does	Example
np.mean()	Average of all values	np.mean([1,2,3]) → 2.0
np.median()	Middle value (better for outliers)	np.median([1,2,100]) → 2.0
np.min() / np.max()	Smallest / Largest value	np.max([5,3,9]) → 9
np.sum()	Total of all values	np.sum([1,2,3]) → 6
np.std()	How spread out the data is	Low = consistent, High = scattered

• A vector = one row of numbers (one data point).
• A matrix = many rows stacked (your whole dataset).
• Understanding these basics is essential before building any ML model.