Lesson 4.1 – Descriptive Statistics | Mean, Median, Variance & Standard Deviation

Learning Objectives

After completing this lesson, you will be able to:

• Understand the concept of Descriptive Statistics.
• Calculate Mean and Median.
• Understand Variance and Standard Deviation.
• Interpret measures of central tendency and data dispersion.
• Apply descriptive statistics to solve business problems.

Introduction

Descriptive Statistics is the branch of statistics that summarizes, organizes, and describes the main characteristics of a dataset. Instead of analyzing every individual value, descriptive statistics provide a simple summary using numerical measures and visualizations.

Business analysts use descriptive statistics to understand customer behavior, sales performance, employee productivity, financial performance, and operational efficiency before performing advanced analysis.

What is Descriptive Statistics?

Descriptive Statistics helps answer questions such as:

• What is the average sales value?
• What is the typical customer age?
• How much do sales vary?
• Is the data consistent or highly scattered?

The four most commonly used descriptive statistics are Mean, Median, Variance, and Standard Deviation.

Mean (Average)

The Mean is the arithmetic average of all values in a dataset.

Formula

Mean = Sum of all values ÷ Number of observations

Example

Monthly sales are:

₹40,000, ₹45,000, ₹50,000, ₹55,000 and ₹60,000

Mean = (40,000 + 45,000 + 50,000 + 55,000 + 60,000) ÷ 5 = ₹50,000

Advantages

• Easy to calculate.
• Uses every value in the dataset.
• Useful for normally distributed data.

Limitation

Mean is affected by extreme values (outliers).

Median (Middle Value)

The Median is the middle value after arranging data in ascending or descending order.

Example

Employee salaries:

₹20,000, ₹22,000, ₹25,000, ₹28,000, ₹1,00,000

Median = ₹25,000

The median provides a better representation because the ₹1,00,000 salary is an outlier.

Advantages

• Not affected by outliers.
• Represents the typical value.
• Useful for skewed datasets.

Variance

Variance measures how far data values are spread from the mean.

Formula

Variance = Σ (x − Mean)² ÷ n

Interpretation

• Low Variance → Data values are close together.
• High Variance → Data values are widely spread.

Example

Two stores have the same average daily sales of ₹50,000.

• Store A sells between ₹49,000 and ₹51,000 every day.
• Store B sells between ₹20,000 and ₹80,000 every day.

Store B has much higher variance because its sales fluctuate significantly.

Standard Deviation

Standard Deviation is the square root of variance and measures the average distance of data values from the mean.

Formula

Standard Deviation = √Variance

Interpretation

• Low Standard Deviation indicates consistent data.
• High Standard Deviation indicates greater variability.

Example

If the average delivery time is 30 minutes:

• Standard Deviation = 2 minutes → Deliveries are highly consistent.
• Standard Deviation = 10 minutes → Delivery performance is unpredictable.

Comparison of Mean, Median, Variance, and Standard Deviation

Business Applications

• Analyze customer spending behavior.
• Evaluate employee salaries.
• Monitor product quality.
• Measure financial risk.
• Track sales performance.
• Evaluate delivery consistency.
• Create business dashboards and KPIs.

Real-World Example

An online retail company analyzes monthly sales using descriptive statistics.

• Mean identifies average monthly sales.
• Median identifies the typical sales value.
• Variance measures sales fluctuations.
• Standard Deviation helps managers understand sales consistency.

These insights help management forecast demand, allocate budgets, and improve business planning.

Key Takeaways

• Descriptive Statistics summarizes data.
• Mean and Median measure central tendency.
• Variance and Standard Deviation measure variability.
• Median is preferred when data contains outliers.
• Descriptive statistics provide the foundation for Business Analytics and Machine Learning.

Lesson Summary

Descriptive Statistics provides simple yet powerful techniques for understanding business data. Mean, Median, Variance, and Standard Deviation help analysts summarize information, measure consistency, identify unusual patterns, and support better business decisions. Every Business Analytics project begins with descriptive statistical analysis before moving to predictive or advanced analytics.

What’s Next?

In the next lesson, you will learn Probability Fundamentals for Business Analytics and understand how probability helps businesses make decisions under uncertainty.