Question

what is the standard deviation of the numbers 4, 5, and 6?

Explanation:

Step1: Calculate the mean

The mean $\bar{x}=\frac{4 + 5+6}{3}=\frac{15}{3}=5$.

Step2: Calculate the squared - differences

$(4 - 5)^2=(-1)^2 = 1$, $(5 - 5)^2=0^2 = 0$, $(6 - 5)^2=1^2 = 1$.

Step3: Calculate the variance

The variance $s^2=\frac{(4 - 5)^2+(5 - 5)^2+(6 - 5)^2}{3}=\frac{1 + 0+1}{3}=\frac{2}{3}$.

Step4: Calculate the standard deviation

The standard deviation $s=\sqrt{\frac{2}{3}}\approx0.816$.

Answer:

0.816