Question

for the year, brunos monthly dining out expenses were: $200, $220, $210, $230, $210, $205, $215, $225, $210, $205, $230, and $220. what is the standard deviation of his expenses, rounded to the nearest whole number? use the following formula to calculate standard deviation: $sigma=sqrt{\frac{sum_{i = 1}^{n}(x_{i}-\text{mean})^2}{n}}$ where $x_{i}$ is each data point, and $n$ is the number of data points. notice that $sum_{i = 1}^{n}(x_{i}-\text{mean})^2 = 1,100$. $9.57 $11.25 $8.54

Explanation:

Step1: Identify values

We are given that $\sum_{i = 1}^{n}(x_{i}-\text{mean})^2=1100$ and $n = 12$ (since there are 12 months in a year).

Step2: Apply standard - deviation formula

The formula for the standard deviation $\sigma=\sqrt{\frac{\sum_{i = 1}^{n}(x_{i}-\text{mean})^2}{n}}$. Substitute $\sum_{i = 1}^{n}(x_{i}-\text{mean})^2 = 1100$ and $n = 12$ into the formula: $\sigma=\sqrt{\frac{1100}{12}}$.

Step3: Calculate the result

$\frac{1100}{12}\approx91.67$, and $\sqrt{91.67}\approx9.57$.

Answer:

$\$9.57$