students of a class in three subjects, Mathematics, Physics and Chemistry are given below. Which of the three subjects shows the highest variability in marks and which shows the lowest?
We are given,
The mean and standard deviation of Mathematics are 
and 
respectively.
The mean and standard deviation of Physics are 
and 
respectively.
The mean and standard deviation of Chemistry are 
and 
respectively.
Also, we know that coefficient of variation is,
![\[C.V = \frac{{{\text{ Standard deviation }}}}{{{\text{ Mean }}}} \times 100\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-9a6a78f0f2591a16be33848f66982571_l3.png "Rendered by QuickLaTeX.com")
Now,
C.V in Mathematics
![\[ = \frac{{12}}{{42}} \times 100\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-ab98f0d110ca6b2873dac89f4d4b5ad4_l3.png "Rendered by QuickLaTeX.com")
![\[ = 28.57{\text{ }}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-368c51f65a3a0f6f1dc199a4e4fe7bd4_l3.png "Rendered by QuickLaTeX.com")
C.V in Physics
![\[ = \frac{{15}}{{32}} \times 100\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-347786783a1e34676d1b8d85c07cff6c_l3.png "Rendered by QuickLaTeX.com")
![\[ = 46.87\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-ec4ab4e064be47c06eae52df2f5572be_l3.png "Rendered by QuickLaTeX.com")
C.V in Chemistry
![\[ = \frac{{20}}{{40.9}} \times 100\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-5bd7fbeacac12ef9f427d4ac0bd5cb21_l3.png "Rendered by QuickLaTeX.com")
![\[ = 48.89\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-5a8398888cb20ffbabbde4c4ac6a3dbc_l3.png "Rendered by QuickLaTeX.com")
Therefore, out of the three subjects the highest variability in marks is in Chemistry and the highest variability in marks is in Mathematics.