એક વર્ગમાં 60 વિધ્યાર્થીઓ છે એક પરીક્ષામાં તે | vedclass

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Question

Sum of frequencies,

$x-2+x+x^{2}+(x+1)^{2}+2 x+x+1=60$

$2 x^{2}+7 x-60=0$

$(2 x+15)(x-4)=0$

$x=4$

$\begin{array}{|c|c|c|c|c|} \hline x

Vedclass · Accepted Answer

Vedclass · Answer

Sum of frequencies,

$x-2+x+x^{2}+(x+1)^{2}+2 x+x+1=60$

$2 x^{2}+7 x-60=0$

$(2 x+15)(x-4)=0$

$x=4$

$\begin{array}{|c|c|c|c|c|} \hline x _{ i } & f_{i} & d_{i}=x_{i}-3 & f_{i} d_{i} & f_{i} d_{i}^{2} \ \hline 0 & 2 & -3 & -6 & 18 \ \hline 1 & 4 & -2 & -8 & 16 \ \hline 2 & 16 & -1 & -16 & 16 \ \hline A=3 & 25 & 0 & 0 & 0 \ \hline 4 & 8 & 1 & 8 & 8 \ \hline 5 & 5 & 2 & 10 & 20 \ \hline 	ext { Total } & \Sigma f_{i}=60 & & \Sigma f_{i}=-12 & \Sigma f_{i} d_{i}^{2}=78 \ \hline \end{array}$

Mean $=A+\frac{\Sigma f_{i} d_{i}}{\Sigma f_{i}}=3+\left(\frac{-12}{60}ight)=2.8$

Standard Deviation,

$\sigma$=$\sqrt{\frac{\Sigma f_{i} d_{i}^{2}}{\Sigma f_{i}}-\left(\frac{\Sigma f_{i} d_{i}}{\Sigma f_{i}}ight)^{2}}=\sqrt{\frac{78}{60}-\left(\frac{-12}{60}ight)^{2}}=\sqrt{1.3-0.04}=\sqrt{1.26}=1.12$

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