Question

what is the standard deviation of the following sample: 10, 9, 5, 10, 8, 12, 9, 11, 7.
o 2.27
o 2.12
o 4
o 2
o 4.5

Explanation:

Step1: Calculate the mean

$\bar{x}=\frac{10 + 9+5+10+8+12+9+11+7}{9}=\frac{81}{9} = 9$

Step2: Calculate the squared - differences

$(10 - 9)^2=1$, $(9 - 9)^2 = 0$, $(5 - 9)^2=16$, $(10 - 9)^2 = 1$, $(8 - 9)^2=1$, $(12 - 9)^2 = 9$, $(9 - 9)^2=0$, $(11 - 9)^2 = 4$, $(7 - 9)^2=4$

Step3: Calculate the variance

$s^2=\frac{1+0 + 16+1+1+9+0+4+4}{9 - 1}=\frac{36}{8}=4.5$

Step4: Calculate the standard deviation

$s=\sqrt{4.5}\approx2.12$

Answer:

2.12