28,7,7,6,9,9,8,8

 2025-09-13  阅读 48  评论 0

摘要:The numbers provided are: 28, 7, 7, 6, 9, 9, 8, 8. Here's a breakdown of key statistical measures an

The numbers provided are: 28, 7, 7, 6, 9, 9, 8, 8. Here's a breakdown of key statistical measures and insights:

28,7,7,6,9,9,8,8

1. Measures of Central Tendency

  • Mean (Average):
  • ( frac{28 + 7 + 7 + 6 + 9 + 9 + 8 + 8}{8} = frac{82}{8} = 10.25 )

    Note: The outlier (28) heavily influences the mean.

  • Median (Middle Value):
  • Sorted data: 6, 7, 7, 8, 8, 9, 9, 28

    Median = Average of 4th and 5th values = ( frac{8 + 8}{2} = 8 )

  • Mode (Most Frequent):
  • 7, 8, 9 (each appears twice).

    The data is multimodal.

    2. Spread and Outliers

  • Range: ( 28
  • 6 = 22 )
  • The outlier (28) creates a large spread.

  • Interquartile Range (IQR):
  • Q1 (25th percentile): 7
  • Q3 (75th percentile): 9
  • IQR = ( 9
  • 7 = 2 )
  • Outlier threshold: Values outside ( 7
  • 3 = 4 ) or ( 9 + 3 = 12 ).
  • 28 is an outlier.

    3. Data Without the Outlier

    If we exclude 28:

  • New Mean: ( frac{7 + 7 + 6 + 9 + 9 + 8 + 8}{7} approx 7.71 )
  • New Median: 8 (unchanged)
  • Range: ( 9
  • 6 = 3 )
  • Clustering: Data is tightly grouped between 6 and 9.
  • Key Takeaway

    The outlier (28) skews the mean and range significantly. For a more robust measure of central tendency, use the median (8). The modes (7, 8, 9) indicate multiple common values in the dataset.

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