Topic II: Calculating Percentiles

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Topic II Calculating Percentiles

• Calculating Percentiles for Ungrouped Data

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Percentiles - Ungrouped Data

• Once numerical observations are ordered according
  to magnitude, boundaries of a set may be defined
• Definition The Pth percentile of an ordered list
  is the number such that P percent (P) of the
  elements in the list are less than that number.
• Example If a student scores in the 85th
  percentile on a standardised test, then 85 of
  those taking the test had lower scores.

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Percentiles - Ungrouped Data

• The position of the Pth percentile is given by
  the formula P (n 1)/100, rounded to the nearest
  integer, where n is the number of observations in
  the data set.

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Example 1

• Juici Patties collects data on the number of Mega
  Cheese Patties sold each day. For the month of
  June, 2006, the following data were collected

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Example 1 (contd)

• Find the 50th, 60th, 75th, and the 90th
  percentiles.

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Percentiles Grouped Data

• For grouped data
• Step 1 Find the position of the Pth percentile
  (using the same formula on slide 4)
• Step 2 To find the exact point use

L1 lower class boundary of class with
percentile N total number of observations f1
total frequency below percentile class f
frequency of percentile class c class interval
of percentile class
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Example 2

• The frequency table shows a frequency
  distribution of the profits earned by 60 firms.
  Find the 25th and the 50th percentiles.

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Special Percentiles I

• There are some percentiles which have special
  names
• The Median is the 50th percentile
• When the data is divided into 4 equal parts they
  are called Quartiles
• When the data is divided into 10 equal parts they
  are called Deciles

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Quartiles

• The 1st quartile Q1 the 25th percentile
• The 2nd quartile Q2 the 50th percentile
  median)
• The 3rd quartile Q3 the 75th percentile

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Deciles

• The 1st decile D1 10th percentile
• The 2nd decile D2 20th percentile
• The 3rd decile D3 30th percentile
• The 4th decile D4 40th percentile
• The 5th decile D5 50th percentile median
  the 2nd quartile