the number of cars sold at a dealership over several weeks is given below. 14, 23, 31, 29, 33 what is the…

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
Answer
Answer:
A. 6.9
Explanation:
Step1: Calculate the mean ($\mu$)
$\mu=\frac{14 + 23+31+29+33}{5}=\frac{130}{5}=26$
Step2: Calculate $(x_i-\mu)^2$ for each $x_i$
For $x_1 = 14$: $(14 - 26)^2=(-12)^2 = 144$ For $x_2 = 23$: $(23 - 26)^2=(-3)^2 = 9$ For $x_3 = 31$: $(31 - 26)^2=(5)^2 = 25$ For $x_4 = 29$: $(29 - 26)^2=(3)^2 = 9$ For $x_5 = 33$: $(33 - 26)^2=(7)^2 = 49$
Step3: Calculate the sum of $(x_i-\mu)^2$
$144+9+25+9+49 = 236$
Step4: Calculate the standard - deviation ($\sigma$)
$\sigma=\sqrt{\frac{236}{5}}=\sqrt{47.2}\approx6.9$