Percentiles

We will now look at some other measures of location and spread.

• The (100p)th percentile of a population, called , is the number such that of the population and of the population .
  • The 95th percentile:
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  • The 90th percentile:
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  • The 75th percentile:
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  • The 50th percentile:
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  • The 25th percentile:
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  • The 10th percentile:
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• Values which divide the (ordered) data into fourths.
  • Q1 (Lower Quartile): The 25th percentile.
  • Q2 (Median): The 50th percentile.
  • Q3 (Upper Quartile): The 75th percentile.
• Calculating Sample Percentiles
  1. Order the n data values from lowest to highest.
  2. p=.50: Calculate the sample median.
  3. p=.25 or .75:
     • If n is even:
       • Q1 = median of the lower half of the data.
       • Q3 = median of the upper half of the data.
     • If n is odd:
       • Q1 = median of the lower ``half'' of the data (including ).
       • Q3 = median of the upper ``half'' of the data (including ).
  4. :
     • Compute np and round up, call this number m.
     • Use the mth point in order.
• The maximum data value minus the minimum data value: .
• Range (IQR) The value .