Question

as an introduction to probability, a student is asked to roll a fair, six - sided number cube seven times. the results of those seven rolls are shown below. 1,4,4,4,4,6,5 what is the standard deviation of the data? 1.41 1.53 2.33 5

Explanation:

Step1: Calculate the mean

The mean $\bar{x}=\frac{1 + 4+4+4+4+6+5}{7}=\frac{28}{7}=4$.

Step2: Calculate the squared - differences

$(1 - 4)^2=(-3)^2 = 9$, $(4 - 4)^2=0^2 = 0$, $(4 - 4)^2=0^2 = 0$, $(4 - 4)^2=0^2 = 0$, $(4 - 4)^2=0^2 = 0$, $(6 - 4)^2=2^2 = 4$, $(5 - 4)^2=1^2 = 1$.

Step3: Calculate the variance

The variance $s^{2}=\frac{9+0+0+0+0+4+1}{7}=\frac{14}{7}=2$.

Step4: Calculate the standard deviation

The standard deviation $s=\sqrt{2}\approx1.41$.

Answer:

1.41