as an introduction to probability, a student is asked to roll a fair, six - sided number cube seven times…
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
Answer
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
$(1 - 4)^2=(-3)^2 = 9$, $(4 - 4)^2=0$, $(4 - 4)^2=0$, $(4 - 4)^2=0$, $(4 - 4)^2=0$, $(6 - 4)^2=4$, $(5 - 4)^2=1$.
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