Statistics – Variance

variance is defined as the average of Squared differences from mean value.

Combination is defined and given by the following function:

Formula

δ=(Mni)2nδ=∑(M−ni)2n

Where −

  • MM = Mean of items.
  • nn = the number of items considered.
  • nini = items.

Example

Problem Statement:

Find the variance between following data : {600, 470, 170, 430, 300}

Solution:

Step 1: Determine the Mean of the given items.

M=600+470+170+430+3005=19705=394M=600+470+170+430+3005=19705=394

Step 2: Determine Variance

δ=(Mni)2n=(600394)2+(470394)2+(170394)2+(430394)2+(300394)25=(206)2+(76)2+(224)2+(36)2+(94)25=42,436+5,776+50,176+1,296+8,8365=108,5205=(14)(13)(3)(11)(2)(1)=21,704δ=∑(M−ni)2n=(600−394)2+(470−394)2+(170−394)2+(430−394)2+(300−394)25=(206)2+(76)2+(−224)2+(36)2+(−94)25=42,436+5,776+50,176+1,296+8,8365=108,5205=(14)(13)(3)(11)(2)(1)=21,704

As a result, Variance is 21,70421,704.