Question

given the sample, 34, 45, 32, 43, 25, 40, and 33, what is the variance?
\frac{\sum (x - \bar{x})^2}{n - 1}
(round off to two decimal places, as they occur.)
36
42
42.29
49.33

Explanation:

Step1: Calculate mean

$\bar{x}=\frac{34 + 45+32+43+25+40+33}{7}=36$

Step2: Calculate squared - differences

$(34 - 36)^2+(45 - 36)^2+(32 - 36)^2+(43 - 36)^2+(25 - 36)^2+(40 - 36)^2+(33 - 36)^2=275$

Step3: Calculate variance

$Var=\frac{275}{7 - 1}\approx42.29$

Answer:

C. 42.29