37  Mathematical Thinking in Data Analysis

37.1 Introduction

So far, you’ve learned how data analysts think — critically, logically, and creatively.
Now, it’s time to take that one step further by applying a mathematical approach to problem-solving.

Mathematical thinking doesn’t mean you have to be a mathematician.
Instead, it means using logical reasoning and step-by-step analysis to identify relationships, recognize patterns, and arrive at informed conclusions.
It’s a mindset that helps you break down complex problems into manageable parts and select the best analytical tools for the job.

37.2 What Is Mathematical Thinking?

Mathematical thinking involves: - Breaking a problem into smaller, logical steps.
- Identifying the relationships between data points.
- Using quantitative reasoning to analyze outcomes.
- Applying the most suitable tools and methods for analysis.

This kind of thinking allows analysts to move from abstract problems to clear, actionable insights — and it’s essential for choosing the right analytical approach.

37.3 Choosing the Right Tool for the Data

A major part of mathematical thinking is knowing which tool fits your data.
One key factor to consider is the size and complexity of the dataset.

37.3.1 Small Data

• Definition: Specific, focused datasets covering a short period of time or limited metrics.
  
• Example: Tracking how much water you drink each day or the number of website visits per week.
  
• Use Case: Helpful for making daily or small-scale decisions.
  
• Tool: Spreadsheets (Google Sheets or Excel) are ideal for analyzing small datasets, creating charts, and running simple calculations.

37.3.2 Big Data

• Definition: Large, complex datasets that cover longer time periods and contain millions of records.
  
• Example: Hospital admission data over several years or customer transactions across thousands of stores.
  
• Use Case: Useful for answering strategic, large-scale questions and identifying long-term trends.
  
• Tool: SQL (Structured Query Language) is preferred because it efficiently handles, filters, and aggregates large datasets.

37.4 Example: Mathematical Thinking in Action

Let’s look at how a hospital could apply mathematical thinking to solve a real-world problem.

37.4.1 Scenario: Optimizing Hospital Bed Usage

A hospital is experiencing uneven bed utilization — sometimes beds are overused, and other times, too many remain empty.
To solve this, the hospital’s data analysts define their goal as bed optimization — ensuring that enough beds are available for patients without wasting space and resources.

37.4.2 Step 1: Identify Key Variables

The analysts identify metrics that can reveal usage patterns: - Total number of inpatient days
- Total number of available beds
- Bed occupancy rate (BOR) — a metric that measures how efficiently beds are being used.

37.4.3 Step 2: Apply a Formula

They use the bed occupancy rate formula:

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This formula helps the analysts quantify how often hospital beds are occupied over a given period.

37.4.4 Step 3: Select the Right Tool

Because hospitals collect massive amounts of data across departments and timeframes, spreadsheets would be inefficient.
Instead, analysts use SQL to: - Query large patient datasets.
- Calculate occupancy rates over time.
- Identify trends, such as days or months when beds are consistently underused.

37.4.5 Step 4: Interpret the Results

The analysis reveals that many beds remain unused most of the time.
With this insight, hospital leaders decide to: - Reduce the number of beds to cut costs.
- Redirect savings toward purchasing protective equipment and improving patient care.

Through logical analysis and quantitative reasoning, the hospital makes a data-driven decision that saves resources and improves efficiency.

37.5 Why Mathematical Thinking Matters

Mathematical thinking empowers data analysts to: - Recognize the relationships and patterns in data.
- Use logical reasoning to evaluate options.
- Choose the best tools and methods for each task.
- Turn raw data into insightful, evidence-based decisions.

It’s not about memorizing formulas — it’s about applying structure, reasoning, and precision to every analytical problem.

37.6 Key Takeaways

• Mathematical thinking helps analysts logically approach complex problems and reveal new insights.
  
• Small data is ideal for short-term decisions and can be handled using spreadsheets.
  
• Big data supports large-scale strategic decisions and often requires SQL for analysis.
  
• Using formulas like the bed occupancy rate demonstrates how metrics turn raw data into actionable insights.
  
• Mathematical reasoning ensures decisions are objective, efficient, and data-driven.

🎯 Up next, you’ll learn the basics of spreadsheets — the foundational tool that will help you apply everything you’ve learned so far to real-world data analysis tasks.