Question

find standard deviation

Answer 1

Answer:

$\begin{array}{|c|c|c|c|c|c|}\cline{1-6}\sf Marks\;(x)& \sf Frequency(F)&\sf x-A=dx&\sf dx^{2}&\sf Fdx^{2}& \sf Fdx\\\cline{1-6}40&2&40-50=-10&100&200&-20\\45&2&45-50=-5&25&50&-10\\ \sf(A)=50&5&50-50=0&0&0&0\\55&3&\sf55-50=5&25&75&15\\60&2&60-50=10&100&200&20\\\cline{1-6} \sf Total&\sf N=\sum\limits\: F= 14&&&\sf \sum\limits\: Fdx^{2}=525&\sf \sum\limits\; Fdx=5\\\cline{1-6}\end{array}$

$\implies \sf Standard\;Deviation\;(\sigma)=\sqrt{\dfrac{\sum\limits Fdx^{2}}{\sum\limits F}-\Bigg(\dfrac{\sum\;\limits Fdx}{\sum\limits F}\Bigg)^{2}}\\ \\ \\ \implies \sf Standard\;Deviation\;(\sigma)=\sqrt{\dfrac{525}{14}-\Bigg(\dfrac{5}{14}\Bigg)^{2}}\\ \\ \\ \implies \sf Standard\;Deviation\;(\sigma)=\sqrt{37.5-\Bigg(\dfrac{25}{196}\Bigg)}\\ \\ \\ \implies \sf Standard\;Deviation\;(\sigma)=\sqrt{37.5-0.12}\\ \\ \\ \implies \sf Standard\;Deviation\;(\sigma)=\sqrt{37.38}$

$\implies \sf Standard\;Deviation\;(\sigma)=6.11$

Hence, Standard Deviation = 6.11.

Answer 2

I have done it in 2 methods.

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