the test scores of a geometry class are given below. 90, 75, 72, 88, 85. the teacher wants to find the…

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 -6 16 258

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 -6 16 258

Answer

Explanation:

Step1: Calculate the mean $\mu$

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

Step2: Calculate $(x_1-\mu)^2+(x_2 - \mu)^2+(x_3-\mu)^2+(x_4-\mu)^2+(x_5-\mu)^2$

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

Answer:

258