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 + dots + (x_n - mu)^2}{n}})
(\bigcirc) 6.9
(\boldsymbol{\times}) 12.4
(\bigcirc) 15.4
(\bigcirc) 47.2

Explanation:

Step1: Calculate population mean $\mu$

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

Step2: Compute squared deviations

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

Step3: Sum squared deviations

$144 + 9 + 25 + 9 + 49 = 236$

Step4: Calculate variance

$\text{Variance} = \frac{236}{5} = 47.2$

Step5: Find standard deviation

$\sigma = \sqrt{47.2} \approx 6.9$

Answer:

6.9