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The variable $X$ takes two values $x_{1}$ and $x_{2}$ with frequencies $f_{1}$ and $f_{2}$ respectively. If $σ$ denotes the standard deviation of $X,$ then $σ^{2} =$

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f12x12+f22x22f1+f2−f1x1+f2x2f1+f22

f1f2f1+f22x1−x22

f1f2f1−f22x1−x22

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Correct option is B

We have, σ2=f1x12+f2x22f1+f2−f1x1+f2x2f1+f22⇒σ2=1f1+f22f12x12+f22x22+f1f2x12+x22−f12x12−f22x22−2f1f2x1x2⇒σ2=f1f2f1+f22x1−x22

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The variable X takes two values x1 and x2 with frequencies f1 and f2 respectively. If σ denotes the standard deviation of X, then σ2=

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The variable $X$ takes two values $x_{1}$ and $x_{2}$ with frequencies $f_{1}$ and $f_{2}$ respectively. If $σ$ denotes the standard deviation of $X,$ then $σ^{2} =$