MathIsimple
Lesson 6.2: Statistical Analysis & Decision Making

Master Statistical Analysis & Decision Making

Make data-driven decisions! Learn to analyze statistical data, interpret results, and use evidence to make informed choices in real-world situations.

Learning Objectives

Analyze statistical data effectively
Interpret statistical results
Make evidence-based decisions
Evaluate data reliability

Data Analysis Process

Data Collection

• Identify the question or problem

• Determine what data is needed

• Choose appropriate sampling method

• Ensure data quality and reliability

Data Analysis

• Calculate statistical measures

• Identify patterns and trends

• Look for outliers and anomalies

• Compare different data sets

Interpretation

• Understand what the data means

• Consider context and limitations

• Identify relationships and correlations

• Draw meaningful conclusions

Decision Making

• Use evidence to support decisions

• Consider multiple options

• Evaluate risks and benefits

• Communicate findings clearly

Case Study: School Performance Analysis

Scenario: Comparing Two Teaching Methods

Problem: A school wants to decide which teaching method is more effective. They test Method A with 30 students and Method B with 30 students. Here are the results:

Method A Results:

Mean: 78, Median: 80, Range: 25, Standard Deviation: 8.2

Method B Results:

Mean: 82, Median: 85, Range: 20, Standard Deviation: 6.5

Analysis:

  • • Method B has higher mean and median scores
  • • Method B has smaller range and standard deviation (more consistent)
  • • Method B appears to be more effective overall

Decision: Recommend Method B for implementation

Risk Assessment & Decision Making

Example: Investment Decision

Scenario: You have $1000 to invest. Option A has 70% chance of 20% return, 30% chance of -10% loss. Option B has 60% chance of 15% return, 40% chance of -5% loss.

Expected Value Calculation:

Option A: 0.7 × 200 + 0.3 × (-100) = 140 - 30 = $110

Option B: 0.6 × 150 + 0.4 × (-50) = 90 - 20 = $70

Risk Analysis:

  • • Option A has higher expected return but higher risk
  • • Option B has lower expected return but lower risk
  • • Consider your risk tolerance

Decision Framework:

If you prefer higher returns and can accept risk: Choose A

If you prefer stability and lower risk: Choose B

Advanced Statistical Methods

Hypothesis Testing

Process:

1. State hypothesis 2. Collect data 3. Test significance

Use: Making decisions based on statistical evidence

Confidence Intervals

Definition:

Range of values with specified confidence level

Use: Estimating population parameters from sample data

Real-world Applications

Business & Marketing

Market Research

Customer preference analysis

Product launch decisions and pricing strategies

Healthcare & Medicine

Clinical Research

Treatment effectiveness studies

Public health policy and disease prevention

Technology & Data Science

Machine Learning

Model validation and performance

A/B testing and user experience optimization