Central Tendency:Mean , Median, Mode


Central Tendency: Measures of central tendency identify the center, or average of a data set. This central point can then be used to represent the expected value in the data set.

There are three measures for central tendency:

  1. Mean
  2. Median
  3. Mode

Mean further can be categorized into 3:

  1. Arithmetic Mean: Arithmetic mean is commonly known as average. To compute Arithmetic mean sum all the observations in the data set divided by the number of observations.                                                                                                                               Mean_111
  2. Geometric Mean: Geometric mean is a kind of average, which is used to calculate average growth rate or interest rate over a given time period. A very common use of Geometric mean is calculation of investment return over multiple periods. The formula for geometric mean is:                                         Mean_112 Geometric mean can be calculated only for positive numbers.
  1. Harmonic Mean: Harmonic mean is kind of average which is calculated by dividing the number of observations with the sum of reciprocal of each observation. Harmonic mean is used for certain computations, such as the average cost of shares purchased over time.


For a data set with unequal values: Harmonic Mean < Geometric mean < Arithmetic Mean. As the spread in values increases the difference between different means increases. For a data set with all the observations having same value, HM=GM=AM.

Median: Median is the middle number in a sorted data set.  To determine the median value in a sequence of numbers, the numbers must first be arranged in value order from lowest to highest. If there is an odd amount of numbers, the median value is the number that is in the middle, with the same amount of numbers below and above. If there is an even amount of numbers in the list, the middle pair must be determined, added together and divided by two to find the median value.

Mode: The mode is the value that occurs most frequently in a data set. A data set may have more than one mode or even no mode. When a distribution has one value that appears most frequently, it is said to be uni-modal. When a set of data has two or three values that occur most frequently, it is said to be bi-modal or tri-modal, respectively.





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