Question

a contractor records all of the bedroom areas, in square feet, of a five - bedroom house as: 100, 100, 120, 120, 180. what is the variance? what is the standard deviation?

Explanation:

Step1: Calculate the mean

$\bar{x}=\frac{100 + 100+120+120+180}{5}=\frac{620}{5}=124$

Step2: Calculate the squared - differences

$(100 - 124)^2=(- 24)^2 = 576$, $(100 - 124)^2=(-24)^2 = 576$, $(120 - 124)^2=(-4)^2 = 16$, $(120 - 124)^2=(-4)^2 = 16$, $(180 - 124)^2=(56)^2 = 3136$

Step3: Calculate the variance

$Var(X)=\frac{576+576 + 16+16+3136}{5}=\frac{4320}{5}=864$

Step4: Calculate the standard deviation

$\sigma=\sqrt{864}\approx29.4$

Answer:

Variance: 864
Standard deviation: 29.4