Answer
a) True.
b)True.
c) False.
d)True.
e)False.
Work Step by Step
Standard deviation: $\sqrt{\frac{\sum(x-\mu)^2}{n}}.$
a)Mean:$\mu=\frac{\sum x}{n}=\frac{25\cdot20}{25}=20$ Hence all $x-\mu=0$, hence the standard deviation is 0, hence the statement is true.
b) True, because in the formula of standard deviation, all values are non-negative, hence it cannot be less than 0.
c) $Variance=(standard \ deviation)^2=(3 \ kg)^2=9 \ kg^2\ne9 \ kg$, hence the statement is false.
d) $standard \ deviation=\sqrt{variance}=\sqrt{16 \ sec^2}= 4 \ sec.$ Hence the statement is true.
e)$Variance=(standard \ deviation)^2=(25 \ cm)^2=625 \ cm^2\ne5 \ cm^2$, hence the statement is false.
