Question

a sample of data was collected below. calculate the sample standard deviation, to one decimal place.
|x|
|30|
|5|
|27|
|8|
|3|

Explanation:

Step1: Calculate the mean

The data set is \(x = \{30, 5, 27, 8, 3\}\). The mean \(\bar{x}=\frac{30 + 5+27+8+3}{5}=\frac{73}{5}=14.6\)

Step2: Calculate the squared - differences

\((30 - 14.6)^2=(15.4)^2 = 237.16\), \((5 - 14.6)^2=(-9.6)^2 = 92.16\), \((27 - 14.6)^2=(12.4)^2 = 153.76\), \((8 - 14.6)^2=(-6.6)^2 = 43.56\), \((3 - 14.6)^2=(-11.6)^2 = 134.56\)

Step3: Calculate the sum of squared - differences

\(S=\sum_{i = 1}^{n}(x_i-\bar{x})^2=237.16+92.16+153.76+43.56+134.56 = 661.2\)

Step4: Calculate the sample variance

The sample variance \(s^2=\frac{S}{n - 1}\), where \(n = 5\), so \(s^2=\frac{661.2}{4}=165.3\)

Step5: Calculate the sample standard deviation

The sample standard deviation \(s=\sqrt{s^2}=\sqrt{165.3}\approx12.9\)

Answer:

12.9