9: measures of location and other measures of dispersion

• Values below which a specified fraction are percentage of a given observation in a data set must fall

  The measures of location or fractiles
• Three types of fractiles

  1. Percentile
  2. Decile
  3. Quartiles
• 99 score points which divide a distribution of scores into 100 equal parts

  Percentiles
• How are percentiles denoted

  P1, P2, P3,.... P99
• LCBpi stands for

  Lower class boundary of the pith class
• C stands for

  Class size
• CFpre stands for

  Cumulative frequency of the class before the Pith lass
• f stands for

  Frequency of the Pith class
• Pith class stands for

  Class where the CF is greater than or equal to in / 100 for the first time
• First step in calculating the percentile

  Arrange in ascending order
• 9 score points which divide the array of observations into 10 equal parts

  Deciles
• Deciles are denoted by

  D1,D2,D3,... D9
• D1 is read us


  First decile
• D1 as the first decile is the value below which percent of the values fall

  10%
• Three score points which divide the array of observations into four equal parts

  Quartiles
• Quartiles are denoted by

  Q1,Q2,Q3
• What are the commonly used measures of dispersion other than MAD and standard deviation

  1. Coefficient of variation
  2. Inter-quartile range
  3. Quartile deviation
• Another measure of dispersion which is defined as the ratio of the standard deviation to its mean

  Coefficient of variation
• the difference between the third quartile and the first quartile

  Inter- quartile range or IQR
• half the inter-quartile range

  Quartile deviation or QD