Question

fiona recorded the number of miles she biked each day last week as shown below. 4, 7, 4, 10, 5. the mean is given by m = 6. which equation shows the variance for the number of miles fiona biked last week? s² = ((4 - 6)²+(7 - 6)²+(4 - 6)²+(10 - 6)²+(5 - 6)²)/6; σ = √(((4 - 6)²+(7 - 6)²+(4 - 6)²+(10 - 6)²+(5 - 6)²)/5); s = √(((4 - 6)²+(7 - 6)²+(4 - 6)²+(10 - 6)²+(5 - 6)²)/4); σ² = ((4 - 6)²+(7 - 6)²+(4 - 6)²+(10 - 6)²+(5 - 6)²)/5

Explanation:

Step1: Recall variance formula

The formula for the variance $s^{2}$ of a sample of data points $x_1,x_2,\cdots,x_n$ with mean $\bar{x}$ is $s^{2}=\frac{\sum_{i = 1}^{n}(x_i-\bar{x})^{2}}{n - 1}$ (for sample variance). Here, $n = 5$ data - points ($4,7,4,10,5$) and $\bar{x}=6$.

Step2: Identify correct formula among options

We calculate the sum of the squared differences $(x_i - 6)^2$ for each $x_i$ value. The sum is $(4 - 6)^2+(7 - 6)^2+(4 - 6)^2+(10 - 6)^2+(5 - 6)^2$. Since $n = 5$, for sample variance, we divide by $n-1=4$. But if we assume this is the population variance $\sigma^{2}$, we divide by $n = 5$.
The formula for population variance $\sigma^{2}=\frac{(4 - 6)^2+(7 - 6)^2+(4 - 6)^2+(10 - 6)^2+(5 - 6)^2}{5}$

Answer:

$\sigma^{2}=\frac{(4 - 6)^2+(7 - 6)^2+(4 - 6)^2+(10 - 6)^2+(5 - 6)^2}{5}$ (assuming population variance, and this is the correct form among the given options as the others are either for standard - deviation or have incorrect denominators)