title: Bossy Brocci's Stats & Data Teacher Workbook: Types of Data Displays, Measures of Central Tendency: Mean, Median, Mode & Range; Measures of Variation ... Graphs & Misinterpreting Circle Graphs
author:  Chris Brocci 
description: Mr. Brocci (pronounced "brawsee") teaches Math &amp; Science in western North Carolina. He is the creator of the student-enabling &amp; teacher-friendly series of 'Bossy Broccis' Math &amp; Big Science workbooks. Mr. Brocci's Brocci's 10 years of higher education includes stops at Cornell, SUNY Stony Brook, SUNY Albany, U. Maryland and Mars Hill College. He holds a B.A. in History, a B.S. in Chemistry and a M.S. in Organic Chemistry. Mr. Brocci has earned Phi Beta Kappa &amp; Summa Cum Laude distinctions, and been awarded for his achievement in Calculus, Chemistry &amp; Physics. He has won teaching awards at the school, county and university levels. His greatest honor, however, has simply been to teach. Learning improves one's chances in life  and Mr. Brocci created these workbooks to do just that.
zlib_text: NODE6 (E)\DATA\2014\KOTA\JEE-ADVANCED\SMP\MATHS\UNIT#02\ENG\PART-2\04-STATISTICS\1.THEORY
  JEE-Mathematics
  E
  33
  STATISTICS
  MEASURES OF CENTRAL TENDENCY :
  An average value or a central value of a distribution is the value of variable which is representative of the
  entire distribution, this representative value are called the measures of central tendency.
  Generally the following five measures of central tendency.
  (a)
  Mathematical average
  (i) Arithmetic mean            (ii) Geometric mean         (iii) Harmonic mean
  (b)
  Positional average
  (i) Median
               (ii) Mode
  1 .
  ARITHMETIC MEAN :
  ( i )
  For ungrouped dist. : If x1, x2, ...... xn are n values of variate xi then their A.M. x  is defined as
  x  = 
  
  
  
  1
  2
  n
  x
  x
  .....
  x
  n
   = 
  
  n
  i
  i 1
  x
  n
  
  xi = n x
  (ii) For ungrouped and grouped freq. dist. : If x1, x2, .... xn are values of variate with corresponding
  frequencies f1, f2, ... fn then their A.M. is given by
  x  = 
  
  
  
  
  
  
  1
  1
  2
  2
  n
  n
  1
  2
  n
  f x
  f x
  ....
  f x
  f
  f
  ....
  f
   = 
  
  