Standard deviation = sqrt ( average ( (X-mean)^2 ) ) for all X

= sqrt ( sum ( 0.1*(7-9.5)^2 + 0.1*(8-9.5)^2 + 0.3*(9-9.5)^2 + 0.2*(10-9.5)^2 + 0.3*(11-9.5)^2 ) )

= sqrt ( 0.625 + 0.225 + 0.075 + 0.05 + 0.675 )

= 1.3

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