Question

what is the standard deviation of the numbers 3, 5, and 7? 0.816 1.63 2.67 1.00

Explanation:

Step1: Calculate the mean

The mean $\bar{x}=\frac{3 + 5+7}{3}=\frac{15}{3}=5$.

Step2: Calculate the squared - differences

$(3 - 5)^2=(-2)^2 = 4$, $(5 - 5)^2=0^2 = 0$, $(7 - 5)^2=2^2 = 4$.

Step3: Calculate the variance

The variance $s^2=\frac{4 + 0+4}{3}=\frac{8}{3}\approx2.67$.

Step4: Calculate the standard deviation

The standard deviation $s=\sqrt{\frac{8}{3}}\approx1.63$.

Answer:

$1.63$