Central Trend Measures

Central Trend Measures

1. determine the position of a value relative to a data set considered representative for the total observatories

   • · represented by a single figure
   • · objective and defined by an algebraic formula
   • · descriptive of the data
   • · should not be a mathematical abstraction
   • · be easy to calculate
   • · depend on each of the elements of the group
   • · should not be affected too much by some or a few values
   • · must have co-responsibility in sampling
   • · be easy to use to calculate later mathematics

2. Mean

   • arithmetic mean:
     • sum of all the observed values divided by the total number of observations
       • may be
         • data not grouped
         • data grouped
   • mean quadratic
     • the square root of the arithmetic mean of the squares of the values taken by the root
       • is calculated for
         • data grouped
         • data not grouped
   • geometric mean
     • the nth root of the production of the values taken by the variable Mo
       • is calculated for
         • data not grouped
         • data grouped
   • mean harmonic
     • given a series of data the inverse of the harmonic mean is equal to the arithmetic mean of the inverse of the values of the variable
       • is calculated for
         • data not grouped
         • data grouped

3. mode

   • of defines as
     • the value of the most repeated variable
       • -unimode -bimode -multimode

4. average

   • of defines as
     • the central value is symbolized Me
       • is calculated for
         • data not grouped
         • data grouped

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