Question

find the standard deviation for the group of data items. 8, 9, 10, 11, 12 the standard deviation is (round to two decimal places as needed.)

Explanation:

Step1: Calculate the mean

The mean $\bar{x}=\frac{8 + 9+10 + 11+12}{5}=\frac{50}{5}=10$

Step2: Calculate the squared differences

$(8 - 10)^2=(-2)^2 = 4$; $(9 - 10)^2=(-1)^2 = 1$; $(10 - 10)^2=0^2 = 0$; $(11 - 10)^2=1^2 = 1$; $(12 - 10)^2=2^2 = 4$

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:

$1.41$