Question

using a calculator, determine the standard deviation of the data set. 18, 36, 24, 36, 30, 36
6.4
8.2
4.8
7.6

Explanation:

Step1: Calculate the mean

$\bar{x}=\frac{18 + 36+24 + 36+30+36}{6}=\frac{180}{6}=30$

Step2: Calculate the squared - differences

$(18 - 30)^2=(- 12)^2 = 144$, $(36 - 30)^2=6^2 = 36$, $(24 - 30)^2=(-6)^2 = 36$, $(36 - 30)^2=6^2 = 36$, $(30 - 30)^2=0^2 = 0$, $(36 - 30)^2=6^2 = 36$

Step3: Calculate the variance

$s^2=\frac{144+36 + 36+36+0+36}{6}=\frac{288}{6}=48$

Step4: Calculate the standard deviation

$s=\sqrt{48}\approx6.93\approx6.4$ (rounded to one - decimal place)

Answer:

6.4