Question

the number of cars sold at a dealership over several weeks is given below. 14, 23, 31, 29, 33 what is the standard deviation for this set of population data? standard deviation: $sigma=sqrt{\frac{(x_1 - mu)^2+(x_2 - mu)^2+cdots+(x_n - mu)^2}{n}}$ 6.9 12.4 15.4 47.2

Explanation:

Step1: Calculate the mean $\mu$

$\mu=\frac{14 + 23+31+29+33}{5}=\frac{130}{5}=26$

Step2: Calculate the squared - differences

$(14 - 26)^2=(-12)^2 = 144$
$(23 - 26)^2=(-3)^2 = 9$
$(31 - 26)^2=(5)^2 = 25$
$(29 - 26)^2=(3)^2 = 9$
$(33 - 26)^2=(7)^2 = 49$

Step3: Calculate the variance

Variance $=\frac{144 + 9+25+9+49}{5}=\frac{236}{5}=47.2$

Step4: Calculate the standard deviation

$\sigma=\sqrt{47.2}\approx6.9$

Answer:

6.9