Question

a teacher recorded all of his students’ grades on the final exam as: 62, 77, 78, 80, 82, 82, 83, 84, 85, 87, 89, 95. consider the formulas: a: $s^{2}=\frac{(x_{1}-overline{x})^{2}+(x_{2}-overline{x})^{2}+cdots+(x_{n}-overline{x})^{2}}{n - 1}$, b: $s=sqrt{\frac{(x_{1}-overline{x})^{2}+(x_{2}-overline{x})^{2}+cdots+(x_{n}-overline{x})^{2}}{n - 1}}$, c: $sigma^{2}=\frac{(x_{1}-mu)^{2}+(x_{2}-mu)^{2}+cdots+(x_{n}-mu)^{2}}{n}$, d: $sigma=sqrt{\frac{(x_{1}-mu)^{2}+(x_{2}-mu)^{2}+cdots+(x_{n}-mu)^{2}}{n}}$

Explanation:

Step1: Identify the data set nature

The teacher recorded all students' grades. So this is the population, not a sample.

Step2: Recall variance and standard - deviation formulas for population

For a population, the variance formula is $\sigma^{2}=\frac{(x_1 - \mu)^{2}+(x_2 - \mu)^{2}+\cdots+(x_N - \mu)^{2}}{N}$ (formula C) and the standard - deviation formula is $\sigma=\sqrt{\frac{(x_1 - \mu)^{2}+(x_2 - \mu)^{2}+\cdots+(x_N - \mu)^{2}}{N}}$ (formula D). Since we want the variance formula for the population, we choose formula C.

Answer:

C