Question

for the year, sams monthly dining - out expenses were $200, $220, $210, $230, $210, $205, $215, $225, $210, $205, $230, and $225. 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}=1100). $12.34 $9.57 $8.54 $11.25

Explanation:

Step1: Identify the number of data - points

There are 10 data - points, so $n = 10$.

Step2: Use the standard deviation formula

The formula for the standard deviation is $s=\sqrt{\frac{\sum_{i = 1}^{n}(x_{i}-\text{mean})^{2}}{n}}$. We are given that $\sum_{i = 1}^{n}(x_{i}-\text{mean})^{2}=1200$. Substitute $n = 10$ into the formula: $s=\sqrt{\frac{1200}{10}}$.

Step3: Calculate the value

First, $\frac{1200}{10}=120$. Then, $s=\sqrt{120}\approx 10.95\approx11$. Since we need to round to the nearest whole number, and among the given options, the closest one to our result is $\$11.25$.

Answer:

$\$11.25$