Measures of central tendency important points. Chapter overview.

 MEASURES OF CENTRAL TENDENCY

1)measures of Central tendency
  •      Mean 
  •      Median
  •      Mode 
2) Mean is of three types 
  • Arithmetic mean
  • Geometric mean and
  • Harmonic mean
A)Arithmetic mean
  •  It is least affected by sampling fluctuations 
  • Extreme values have greater effect on mean.
  •  It is affected due to change of origin and scale
  • The best measure of Central tendency is arithmetic mean

B) Median

  •  It is best measure for qualitative data such as duty intelligence honesty.
  • It is not affected by extreme values. 
  • It can be located graphically through ogive curves.
  • It is affected due to change of origin and scale
C) Mode
  • It is not affected by extreme values it can also be found graphically through Instagram.
  • It can also be used in case of qualitative phenomenon.
  • Mode is the most affected by fluctuations of sampling 
  • Mode is affected due to change of origin and scale.
  • Mode is the most popular measure of Central tendency
Points
  • Geometric mean is useful in the construction of index numbers
  • Harmonic mean is useful in averaging rates ratios speeds and prices
  • harmonic mean is cannot be computed if any value is zero

  • For any set of positive observations AM≥GM≥HM
  • Particularly is all the observations are distinct then AM>GM>HM.
  • If all the observations are equal then, AM=GM=HM.
  • For only two positive numbers, (GM)²=(AM)×(HM).


  • Mean – Median = 1/3 (Mean– Mode)
  • Mode= 3 Median – 2 Mean
  • Median – Mode = 2/3(Mean – Mode)


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