Question

the test scores of a geometry class are given below. 90, 75, 72, 88, 85. the teacher wants to find the variance for the class population. what is the value of the numerator of the calculation of the variance? variance: $sigma^{2}=\frac{(x_{1}-mu)^{2}+(x_{2}-mu)^{2}+cdots+(x_{n}-mu)^{2}}{n}$ -160 16 258

Explanation:

Step1: Calculate the mean

$\mu=\frac{90 + 75+72+88+85}{5}=\frac{410}{5} = 82$

Step2: Calculate the squared - differences

$(90 - 82)^2+(75 - 82)^2+(72 - 82)^2+(88 - 82)^2+(85 - 82)^2$
$=(8)^2+( - 7)^2+( - 10)^2+(6)^2+(3)^2$
$=64 + 49+100+36+9$
$=258$

Answer:

258