Central Tendency


Central Tendency
  • Whenever you measure things of similar nature, a fairly large number of such measurements will tend to cluster around the middle value. Such a value is called a Measure of "Central Tendency" also called as "Measures of Location" or "Statistical Averages".
  • Mean, Mode, Median, Harmonic Mean, Geometric Mean, etc are some of the examples.
  • Mean, Mode and Median are the widely used Central Tendency measures 
Arithmetic Mean
  • Arithmetic Mean (or simply Mean) is simply defined as the sum of all the observations in a data-set divided by the total number of the observations
  • The sample mean is used to estimate the population mean
  • For example, consider these random measurements: 
    • 565, 570, 572, 568, 585 
    • Mean = (565 + 570 + 572 + 568 + 585)/5 = 572
  • CAUTION: When outliers are present in the data, the arithmetic mean is not a reliable measure


Median
  • Median is the middle most observation when data is arranged in the ascending/descending order of magnitude
  • Median = (n + 1) / 2 th value of the in the ordered data-set 
    • where n is the number of observations in the sample
  • For example, consider the random sample data-set
    • 45, 40, 60, 80, 90, 65, 55
    • Data-set arranged in ascending order: 40, 45, 55, 60, 65, 80, 90
    • Median = (7 + 1)/2 = 4th value in the data-set which is 60
    •  
  • NOTE: Median is not affected by outliers
Mode

  • Mode is the value with maximum frequency of occurrence in the given data-set
  • For example, consider the following data-set:
    • 340, 350, 340, 340, 320, 330, 350, 360, 370, 340
    • Mode = 340, since it has maximum occurrence frequency of 4
  • NOTE: Mode is not affected by outliers
  • CAUTION: In few real life scenarios, we can have more than one mode values such as Bi-Modal or Multi-Modal values. In these cases, mode cannot be uniquely determined. 

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