Dispersion Measurements

Dispersion Measurements

1. Take care of

   • The variability of the data
     • By means of
       • Numbers

2. Types

   • Range
     • Smallest and largest value
       • Example: for the numbers 5, 4, 6, 8, 10, 7, 14, 3, 5 the range is 14-3=11
         • Formula
   • Mean deviation
     • Absolute value
       • Example: qualifications of 5 exams: 80, 75, 70, 83 y 85. • Arithmetic mean 78.6. • Mean deviation 4.88.
         • Formula
     • Grouped data
       • Formula
   • Typical deviation
     • Variance
       • Squares
     • Coefficient of variation
       • Quotient
     • Square root
     • Example: qualifications of 5 exams: 80, 70, 65, 90, 85. • Arithmetic mean 78. • Variance 86. • Typical deviation 9.27. • Coefficient 11.88.
       • Formulas
     • Variance, typical deviation and coefficient of variation for grouped data
       • Formulas
   • Interquartile range
     • Semi-interquartile range
       • Average between the first and third quartile
     • Difference between third quartile and first quartile
     • Example: frequency distribution. • Interquartile range 46.43. • Semi-interquartile range 23.215.
       • Formulas
   • Range between percentiles 10-90
     • Difference between P90 and P10
       • Example: frequency distribution. • The range between the 90-10 percentiles is 62.85.
         • Formula
   • Bias of a distribution
     • Lack of symmetry
       • Example: calculate the bias for 40,40, 40, 35, 30, 25, 20, 15. • Arithmetic mean 30.625. • Variance 83.99. • Typical deviation 9.16. • Mode 40. • Bias 1.06.
         • Formula

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