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Understanding the Interquartile Range (IQR)

Aug 13, 2024

Math Lecture: Understanding Interquartile Range (IQR)

Overview

  • Interquartile Range (IQR) measures the spread of the middle 50% of a data set.
  • Range measures the spread of the entire data set.
  • This lecture provides step-by-step examples with odd and even numbered data sets.

Example 1: Odd Numbered Data Set

  1. Arranging Data

    • Ensure data is in ascending order (from least to greatest).
    • Example data set is already ordered.
  2. Finding the Median

    • Median is the middle number of the data set.
    • For 7 numbers: 3 numbers on each side of the median.
    • Median (Q2) is 38 (50th percentile).
  3. Finding Quartiles

    • Lower Quartile (Q1): Middle number of the lower half.
      • Q1 = 32.
    • Upper Quartile (Q3): Middle number of the upper half.
      • Q3 = 50.
  4. Calculating the IQR

    • IQR = Q3 - Q1 = 50 - 32 = 18.
    • Visualize by dividing data into four equal parts.
    • IQR represents the range of the middle 50% of data.

Example 2: Even Numbered Data Set

  1. Arranging Data

    • Verify data is ordered.
  2. Finding the Median

    • For 10 numbers: Break in half, 5 numbers on each side.
    • Median is between two middle numbers (8 and 11).
    • Calculate median: (8 + 11) / 2 = 9.5.
  3. Finding Quartiles

    • Lower Quartile (Q1): Median of lower 5 numbers.
      • Q1 = 6.
    • Upper Quartile (Q3): Median of upper 5 numbers.
      • Q3 = 14.
  4. Calculating the IQR

    • IQR = Q3 - Q1 = 14 - 6 = 8.
    • Visual representation helps understand quartiles and IQR.

Conclusion

  • IQR helps understand the spread of the central 50% of the data.
  • Further resources available in linked videos for additional help with quartiles.
  • Thanks for tuning in!