"Five-number summary and interquartile range"

Overview of the Five-Number Summary and Interquartile Range

  • The five-number summary is a descriptive statistic that provides a quick overview of a dataset. It consists of the following components:
    • Minimum: Lowest data value.
    • Lower Quartile (Q1): The median of the lower half of the data (25th percentile).
    • Median (Q2): Middle value of the ordered data set (50th percentile).
    • Upper Quartile (Q3): The median of the upper half of the data (75th percentile).
    • Maximum: Highest data value.

Steps to Calculate Five-Number Summary

  1. Order the Data: Start with organizing the data from least to greatest.

    Example Data: [51, 51, 53, 57, 57, 63, 64, 70, 73, 76, 77, 79, 81, 83]

  2. Determine the Minimum and Maximum:

    • Minimum: 51
    • Maximum: 83

  3. Calculate the Median:

    • For an ordered list with an odd number of values, the median is the middle value.
    • For even numbers, average the two middle numbers.
    • Given the data above, the median is 70

  4. Find Lower and Upper Quartiles:

    • Lower Quartile (Q1): Median of the lower half (values left of the median).
      • Values: [51, 51, 53, 57, 57, 63, 64]
      • Q1 Calculation: rac{57 + 57}{2} = 57
    • Upper Quartile (Q3): Median of the upper half (values right of the median).
      • Values: [73, 76, 77, 79, 81, 83]
      • Q3 Calculation: rac{79 + 81}{2} = 80

  5. Calculate the Interquartile Range (IQR):

    • IQR = Q3 - Q1
    • IQR Calculation: 80 - 57 = 23

Summary of Results:

  • Minimum: 51
  • Lower Quartile (Q1): 57
  • Median (Q2): 70
  • Upper Quartile (Q3): 80
  • Maximum: 83
  • Interquartile Range (IQR): 23