Question

determine the standard deviation for the following set of data 4, 1, 4, 2, 9, 8, 4, 12

Explanation:

Step1: Calculate the mean

The mean $\bar{x}=\frac{4 + 1+4+2+9+8+4+12}{8}=\frac{44}{8} = 5.5$

Step2: Calculate the squared differences

$(4 - 5.5)^2=(-1.5)^2 = 2.25$; $(1 - 5.5)^2=(-4.5)^2=20.25$; $(4 - 5.5)^2=(-1.5)^2 = 2.25$; $(2 - 5.5)^2=(-3.5)^2 = 12.25$; $(9 - 5.5)^2=(3.5)^2 = 12.25$; $(8 - 5.5)^2=(2.5)^2 = 6.25$; $(4 - 5.5)^2=(-1.5)^2 = 2.25$; $(12 - 5.5)^2=(6.5)^2 = 42.25$

Step3: Calculate the variance

The variance $s^{2}=\frac{2.25+20.25 + 2.25+12.25+12.25+6.25+2.25+42.25}{8}=\frac{98}{8}=12.25$

Step4: Calculate the standard deviation

The standard deviation $s=\sqrt{12.25}=3.5$

Answer:

$3.5$