Question

question for the following set of data, find the sample standard deviation, to the nearest thousandth. 27, 19, 20, 20, 20, 21, 18, 21, 20

Explanation:

Step1: Calculate the mean

The mean $\bar{x}=\frac{27 + 19+20+20+20+21+18+21+20}{9}=\frac{186}{9}\approx20.667$.

Step2: Calculate the squared - differences

$(27 - 20.667)^2=(6.333)^2 = 40.107$; $(19 - 20.667)^2=(-1.667)^2 = 2.779$; $(20 - 20.667)^2=(-0.667)^2 = 0.445$ (this occurs 4 times); $(21 - 20.667)^2=(0.333)^2 = 0.111$ (this occurs 2 times); $(18 - 20.667)^2=(-2.667)^2 = 7.112$.

Step3: Calculate the sum of squared - differences

$S=\ 40.107+2.779 + 4\times0.445+2\times0.111+7.112=40.107+2.779 + 1.78+0.222+7.112=52$.

Step4: Calculate the sample variance

The sample variance $s^{2}=\frac{S}{n - 1}=\frac{52}{9 - 1}=\frac{52}{8}=6.5$.

Step5: Calculate the sample standard deviation

The sample standard deviation $s=\sqrt{6.5}\approx2.549$.

Answer:

$2.549$