Question

a sample was done, collecting the data below. calculate the standard deviation, to one decimal place.
question help: video

Explanation:

Step1: Calculate the mean

The mean $\bar{x}=\frac{1 + 10+13+2+7}{5}=\frac{33}{5}=6.6$

Step2: Calculate the squared differences

$(1 - 6.6)^2=(-5.6)^2 = 31.36$; $(10 - 6.6)^2=(3.4)^2 = 11.56$; $(13 - 6.6)^2=(6.4)^2 = 40.96$; $(2 - 6.6)^2=(-4.6)^2 = 21.16$; $(7 - 6.6)^2=(0.4)^2 = 0.16$

Step3: Calculate the variance

The variance $s^{2}=\frac{31.36+11.56 + 40.96+21.16+0.16}{5 - 1}=\frac{105.2}{4}=26.3$

Step4: Calculate the standard deviation

The standard deviation $s=\sqrt{26.3}\approx5.1$

Answer:

$5.1$