Statistics

Fundamentals

Q. What is Statistics?

📖 Book Definition

Statistics is the science of collecting, organizing, presenting, analyzing, and interpreting data to draw meaningful conclusions and support decision-making.

🎤 Interview Answer

Statistics is the science of learning from data. It helps us convert raw data into meaningful information so that we can make informed decisions under uncertainty.

💡 Layman Explanation

Imagine a school has marks of 5,000 students. Instead of checking every mark individually, statistics helps summarize the data and answer questions like the average marks, top-performing subjects, or pass percentage.

🌍 Real-Life Example

Netflix uses statistics to understand what users watch and recommends shows based on viewing patterns.

⭐ Keywords

Collect → Organize → Present → Analyze → Interpret → Decide

Q. Why do we need Statistics?

Statistics helps us:

• Summarize large amounts of data

• Identify patterns and trends

• Compare groups

• Make predictions

• Support decision-making

💡 Layman Explanation

Raw data alone doesn't tell a story. Statistics converts numbers into useful information.

🌍 Example

An e-commerce company uses statistics to identify its best-selling products and forecast future demand.

Q. What are the major branches of Statistics?

1. Descriptive Statistics

2. Inferential Statistics

Quick Difference

Descriptive Statistics summarizes data.

Inferential Statistics draws conclusions about a population using sample data.

🌍 Example

Descriptive:
Average salary of 100 employees.

Inferential:
Predicting the average salary of all employees using a sample of 100.

Q. What is Descriptive Statistics?

Descriptive Statistics deals with collecting, organizing, summarizing, and presenting data.

Includes

• Mean

• Median

• Mode

• Charts

• Graphs

• Standard Deviation

Example

Finding average marks of students.

Key Point

It describes only the available data.

Q. Can descriptive statistics make predictions?

No

Q. What is Inferential Statistics?

Inferential Statistics uses sample data to make conclusions or predictions about an entire population.

Includes

• Estimation

• Confidence Interval

• Hypothesis Testing

• Regression

Example

Opinion polls predicting election results.

Q. Difference between Descriptive and Inferential Statistics?

Descriptive	Inferential
Describes data	Makes conclusions
No prediction	Prediction possible
Uses complete dataset	Uses sample
Mean, Median	Confidence Interval, Hypothesis Testing

Q. What is Population?

Population is the complete collection of all observations of interest.

Example

All students in BHU.

Interview Question

Can population be infinite?

Answer:
Yes.

Example:
Future customers of Amazon.

Q. What is a Sample?

Answer

A sample is a subset selected from a population.

Example

200 students selected from BHU.

Why use samples?

Population is often too large, expensive, or impossible to study completely.

Q. Difference between Population and Sample?

Population	Sample
Entire group	Subset
Large	Small
Parameter	Statistic

Example

Population:
All Indian voters.

Sample:
5,000 surveyed voters.

Q. What is a Parameter?

Answer

A parameter is a numerical measure describing a population.

Examples

Population Mean (μ)

Population Variance (σ²)

Population Standard Deviation (σ)

Key Point

Usually unknown.

Q. What is a Statistic?