the test scores of a geometry class are given below.\n90, 75, 72, 88, 85\nthe teacher wants to find the…

the test scores of a geometry class are given below.\n90, 75, 72, 88, 85\nthe teacher wants to find the variance for the class population. what is the value of the numerator of the calculation of the variance?\nvariance: $sigma^{2}=\frac{(x_{1}-mu)^{2}+(x_{2}-mu)^{2}+cdots+(x_{n}-mu)^{2}}{n}$\n-160\n-6\n16\n258

the test scores of a geometry class are given below.\n90, 75, 72, 88, 85\nthe teacher wants to find the variance for the class population. what is the value of the numerator of the calculation of the variance?\nvariance: $sigma^{2}=\frac{(x_{1}-mu)^{2}+(x_{2}-mu)^{2}+cdots+(x_{n}-mu)^{2}}{n}$\n-160\n-6\n16\n258

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