Lecture Notes on Histograms and Data Distribution

Key Concepts

• Understanding how to locate key percentiles in a histogram:
  • 25th Percentile (Q1)
  • Median
  • 75th Percentile (Q3)

Total Data Points

• Total Pieces of Data: 403
  • Importance of knowing the total for calculations.

Finding the Median

• Definition: The median is the middle piece of data.
• Calculation:
  • Divide total data points by 2: 403 / 2 = 201.5
  • Round up to find median position: Data Piece Number = 202.
• Finding Median:
  • Cumulative counting in histogram bins:
    • 1st Bin: 36
    • 2nd Bin: 54 (Total: 90)
    • 3rd Bin: 69 (Total: 159)
    • 4th Bin: 81 (Total: 240)
  • Median falls in the range of 25 to less than 30 minutes.
  • Median: 25 up to not including 30 minutes.

Finding Q1 (25th Percentile)

• Definition: Q1 is the median of the lower half of the data.
• Data in Bottom Half: 201 pieces.
• Calculation:
  • Divide bottom data points by 2: 201 / 2 = 100.5
  • Round up to find Q1 position: Data Piece Number = 101.
• Finding Q1:
  • Cumulative counting:
    • 1st Bin: 36
    • 2nd Bin: 54 (Total: 90)
    • 3rd Bin: 69 (Total: 159)
  • Q1 falls in the range of 20 to less than 25 minutes.
  • Q1: 20 up to not including 25 minutes.

Finding Q3 (75th Percentile)

• Definition: Q3 is the median of the upper half of the data.
• Data in Top Half: 201 pieces.
• Calculation:
  • Find Q3 by counting down from the top: 101 pieces from the top.
• Finding Q3:
  • Cumulative counting from the top:
    • Last Bin: 17
    • Next: 21 or 22 (Total: 38)
    • Next: 25 (Total: 63)
    • Remaining needed to reach 101: 43 more pieces.
  • Q3 falls in the range of 35 to less than 40 minutes.
  • Q3: 35 up to not including 40 minutes.

Summary of Key Values

• Q1: 20 up to 25 minutes
• Median: 25 up to 30 minutes
• Q3: 35 up to 40 minutes

Importance

• Understanding these values is crucial for identifying outliers in data distributions when analyzing histograms.

Additional Tasks

• Next Steps: Estimate totals for each histogram bar to practice and apply concepts learned.