Formulas For Venn Diagrams

Formulas To Find Averages In Aptitude

Average is  widely used in statistics also to reduce the calculation in finding the average where the data is huge.Here We will demonstrate the application of the assumed mean to solve some aptitude questions based on averages and weighted averages.Average is the sum of observations divided by the total number of observations.The Average is also known as mean.We use concept of average in our day to day life. Formulas of Averages is very helpfull in Different Examinations.

In this Page Formulas for Averages is given which is useful to solve many problems.

Formulas for Average Logo

Basic Formula for the Venn Diagram

  • Some basic formulas for Venn diagrams of two and three elements.
  • n ( A ∪ B) = n(A ) + n ( B ) – n ( A∩ B)
  • n (A ∪ B ∪ C) = n(A ) + n ( B ) + n (C) – n ( A ∩ B) – n ( B ∩ C) – n ( C ∩ A) + n (A ∩ B ∩ C)
  • And so on, where n( A) = number of elements in set A.
  • After understanding the concept the of venn diagram with diagram, we don’t have to remember the formulas.

Venn Diagram for 2 sets

n ( A ∪ B) = n(A ) + n ( B ) – n ( A∩ B)
Where;
X = number of elements that belong to set A only
Y = number of elements that belong to set B only
Z = number of elements that belong to set A and B both (A ∩ B)
W = number of elements that belong to none of the sets A or B
From the above figure, it is clear that
n(A) = x + z ;
n (B) = y + z ;
n(A ∩ B) = z;
n ( A ∪ B) = x +y+ z.
Total number of elements = x + y + z + w

Venn Diagram for 2 Sets

Venn Diagram for 3 sets

n (A ∪ B ∪ C) = n(A ) + n ( B ) + n (C) – n ( A ∩ B) – n ( B ∩ C) – n ( C ∩ A) + n (A ∩ B ∩ C)

Where, W = number of elements that belong to none of the sets A, B or C

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