find the standard deviation for the group of data items. 10, 11, 12, 13, 14\nthe standard deviation is…
find the standard deviation for the group of data items. 10, 11, 12, 13, 14\nthe standard deviation is \n(round to two decimal places as needed.)
Answer
Explanation:
Step1: Calculate the mean
The mean $\bar{x}=\frac{10 + 11+12+13+14}{5}=\frac{60}{5}=12$.
Step2: Calculate the squared - differences
$(10 - 12)^2=(-2)^2 = 4$, $(11 - 12)^2=(-1)^2 = 1$, $(12 - 12)^2=0^2 = 0$, $(13 - 12)^2=1^2 = 1$, $(14 - 12)^2=2^2 = 4$.
Step3: Calculate the variance
The variance $s^{2}=\frac{4 + 1+0+1+4}{5}=\frac{10}{5}=2$.
Step4: Calculate the standard deviation
The standard deviation $s=\sqrt{2}\approx1.41$.
Answer:
$1.41$