Question

a sample was done, collecting the data below. calculate the standard deviation, to one decimal place. 3 4 15 25 6

Explanation:

Step1: Calculate the mean

The data set is \(3,4,15,25,6\). The mean \(\bar{x}=\frac{3 + 4+15+25+6}{5}=\frac{53}{5}=10.6\)

Step2: Calculate the squared - differences

\((3 - 10.6)^2=(-7.6)^2 = 57.76\), \((4 - 10.6)^2=(-6.6)^2 = 43.56\), \((15 - 10.6)^2=(4.4)^2 = 19.36\), \((25 - 10.6)^2=(14.4)^2 = 207.36\), \((6 - 10.6)^2=(-4.6)^2 = 21.16\)

Step3: Calculate the variance

The variance \(s^{2}=\frac{57.76+43.56 + 19.36+207.36+21.16}{5}=\frac{349.2}{5}=69.84\)

Step4: Calculate the standard deviation

The standard deviation \(s=\sqrt{69.84}\approx8.4\)

Answer:

\(8.4\)