for the following set of data, find the sample standard deviation, to the nearest thousandth. 18, 64, 44…

Explanation:

Step1: Calculate the mean

The mean $\bar{x}=\frac{18 + 64+44+26+17+75+42+63+45}{9}=\frac{394}{9}\approx43.778$.

Step2: Calculate the squared - differences

$(18 - 43.778)^2=(- 25.778)^2 = 664.515$, $(64 - 43.778)^2=(20.222)^2 = 408.939$, $(44 - 43.778)^2=(0.222)^2 = 0.049$, $(26 - 43.778)^2=(-17.778)^2 = 316.065$, $(17 - 43.778)^2=(-26.778)^2 = 716.065$, $(75 - 43.778)^2=(31.222)^2 = 974.815$, $(42 - 43.778)^2=(-1.778)^2 = 3.165$, $(63 - 43.778)^2=(19.222)^2 = 369.499$, $(45 - 43.778)^2=(1.222)^2 = 1.493$.

Step3: Calculate the sum of squared - differences

$S=\sum_{i = 1}^{9}(x_i-\bar{x})^2=664.515 + 408.939+0.049+316.065+716.065+974.815+3.165+369.499+1.493=3454.505$.

Step4: Calculate the sample variance

The sample variance $s^2=\frac{S}{n - 1}=\frac{3454.505}{9 - 1}=\frac{3454.505}{8}=431.813$.

Step5: Calculate the sample standard deviation

The sample standard deviation $s=\sqrt{431.813}\approx20.780$.

Answer:

$20.780$