The session began with a comprehensive overview of box plots and their significance in statistical analysis:

Components of a Box Plot:

• Box (Interquartile Range – IQR)
  • Represents the middle 50% of data
  • Lower boundary: Q1 (25th percentile)
  • Upper boundary: Q3 (75th percentile)
  • Width of box = IQR (Q3 – Q1)
• Median (Q2 – 50th Percentile)
  • Line inside the box representing the middle value
  • Position indicates skewness of distribution
• Whiskers
  • Extend to min/max values within 1.5×IQR range
  • Indicate range of non-outlier data points
• Outliers
  • Individual points beyond whiskers
  • Represent unusual values in the dataset

The session emphasized how box plots reveal distribution characteristics:

Data Spread Analysis:

• Wider box indicates greater variability in middle 50% of data
• Longer whiskers suggest wider overall data range
• Many outliers may indicate abnormal distribution patterns

Box Plot Modifications:

• Multiplying data by a constant > 1 increases IQR and box width
• Adding a constant shifts the entire box plot but preserves shape

Breakout Room 1 led by Pankaj focused on percentile fundamentals:

Definition: A percentile indicates the relative position of a value within a dataset.

Formula for Percentile Calculation:

Where P represents the position of the percentile value, and n is the percentile being calculated.

Relationship to Box Plots:

• 25th percentile (Q1) = Lower edge of box
• 50th percentile (Q2) = Median line
• 75th percentile (Q3) = Upper edge of box

Breakout Room 2 led by Shabry focused on comparative analysis:

Case Study: Class A vs Class B Exam Scores

Comparative Analysis Technique:

1. Compare median positions (central tendency)
2. Compare box widths (IQR/variability)
3. Compare whisker lengths (data spread)
4. Observe presence/absence of outliers
5. Assess skewness patterns

Students practiced by analyzing and interpreting real-world datasets during the session.

Key questions addressed during the session:

• Q: What does the box in a box plot represent?
  A: The box represents the Interquartile Range (IQR), containing the middle 50% of data values.
• Q: How are percentiles different from quartiles?
  A: Quartiles divide data into 4 equal parts, while percentiles divide data into 100 equal parts.
• Q: Can the median be outside the box?
  A: No, the median (50th percentile) always falls within the box.
• Q: How does an outlier affect a box plot?
  A: Outliers are plotted as separate points and don’t affect the whisker length.
• Q: What happens if a dataset has tied values in percentile ranking?
  A: The average rank of tied values is used for accurate percentile calculations.

The instructors discussed real-world applications of box plots and percentiles:

• Data Science & AI
  • Detecting anomalies in training datasets
  • Quality assessment of model predictions
  • Feature distribution analysis for model selection
• Business Analytics
  • Sales performance distribution across regions
  • Customer behavior pattern analysis
  • Financial risk assessment and outlier detection
• Scientific Research
  • Experimental results validation
  • Comparing treatment groups in clinical studies
  • Identifying significant factors in multivariate datasets

Students were encouraged to practice using online tools like Datatab for box plot visualization and analysis.

The session briefly touched on more advanced statistical concepts related to box plots:

• Confidence Intervals
  • Using box plots to visualize confidence levels
  • Relationship between IQR and standard deviation
• Non-parametric Tests
  • Box plots as visual support for Mann-Whitney U test
  • Comparing datasets without normality assumptions
• Violin Plots
  • Extension of box plots showing probability density
  • When to use violin plots vs. traditional box plots

Instructors noted that these advanced concepts would be covered in more detail in future sessions.

The instructors shared valuable resources for further study:

• Practice Resources:
  • Datatab – Online tool for quick box plot visualization
  • Statistical practice datasets shared via email
  • Interactive exercises for self-assessment
• Additional Support:
  • Email queries to bscdelivery@futurense.cm
  • Office hours for one-on-one assistance
  • Peer learning groups established in breakout rooms

For the next session, students should prepare by practicing with the provided datasets and bringing any remaining doubts.