Statistics and Machine Learning Basics

Statistics helps you describe data honestly, and machine learning uses data to make predictions.

Measures of the Centre

What is a "typical" value? There are three common answers:

Here are the daily cups of tea sold at a small dhaba in one week. On Sunday a big group ordered 40 cups:

import pandas as pd

cups = pd.Series([4, 5, 5, 6, 7, 5, 40])
print("Mean:", round(cups.mean(), 2))
print("Median:", cups.median())
print("Mode:", cups.mode().tolist())

Mean: 10.29
Median: 5.0
Mode: [5]

The one unusual day (40) pulls the mean up to about 10, although on most days around 5 cups were sold. The median is not affected.

Measures of Spread

Two classes can have the same average but very different results. Spread tells you how far values are from each other:

• Range: largest minus smallest
• Standard deviation (std): roughly, the typical distance of values from the mean. Small std means values are close together.

marks = pd.Series([35, 42, 50, 55, 63, 68, 77, 82])
print("Mean:", marks.mean())
print("Range:", marks.max() - marks.min())
print("Std:", round(marks.std(), 2))

Mean: 59.0
Range: 47
Std: 16.53

Correlation

Correlation measures how strongly two numbers move together. It goes from -1 to +1:

Study hours and marks for eight students:

df = pd.DataFrame({
    "hours": [1, 2, 3, 4, 5, 6, 7, 8],
    "marks": [35, 42, 50, 55, 63, 68, 77, 82],
})
print(round(df["hours"].corr(df["marks"]), 3))

0.999

A very strong positive correlation. But remember: correlation is not causation. Ice cream sales and cases of sunburn rise together, but ice cream does not cause sunburn; hot weather causes both.

What is Machine Learning?

In normal programming, you write the rules. In machine learning, you give the computer examples, and it finds the rules itself.

Your First Model: Linear Regression

Linear regression draws the best straight line through the data, then uses it to predict new values. We use scikit-learn (pip install scikit-learn):

from sklearn.linear_model import LinearRegression

X = df[["hours"]]   # input features (a table, so double brackets)
y = df["marks"]     # the answer we want to predict

model = LinearRegression()
model.fit(X, y)

print("Slope:", round(model.coef_[0], 2))
print("Intercept:", round(model.intercept_, 2))

new_students = pd.DataFrame({"hours": [9, 2.5]})
print(model.predict(new_students).round(2))

Slope: 6.74
Intercept: 28.68
[89.32 45.52]

The model learned: marks = 28.68 + 6.74 x hours. Each extra hour of study adds about 6.7 marks. A student who studies 9 hours is predicted to get about 89 marks.

Every scikit-learn model follows the same three steps:

1. Create the model: model = LinearRegression()
2. Train it: model.fit(X, y)
3. Predict: model.predict(new_data)

Testing a Model Fairly

A model must be tested on data it has not seen during training, just as an exam should not use the exact homework questions. Split the data first:

from sklearn.model_selection import train_test_split
from sklearn.metrics import r2_score

X_train, X_test, y_train, y_test = train_test_split(
    X, y, test_size=0.25, random_state=42
)
model = LinearRegression().fit(X_train, y_train)
print(r2_score(y_test, model.predict(X_test)))

The R² score shows how well predictions match real values: 1.0 is perfect, and 0 means the model is no better than always guessing the average. With real datasets you would use hundreds or thousands of rows, not eight.

Exercise