Question

The following data points are the yearly salaries (in thousands of dollars) of the \[4\] high school cheerleading coaches in Dakota County.

\[41,46,52,49\]
Find the standard deviation of the data set.
Round your answer to the nearest hundredth.

thousand dollars

Answer 1

The standard deviation of the yearly salaries for the four high school cheerleading coaches is approximately 4.06 thousand dollars, after calculating the mean salary, finding the differences, squaring them, finding the mean of the squares, and taking the square root of that mean.

Step-by-step explanation:

To find the standard deviation of the yearly salaries of the four high school cheerleading coaches, you will first need to calculate the mean (average) salary and then use that to find the variance and standard deviation. Here's a step-by-step guide:

1. Calculate the mean salary: (41 + 46 + 52 + 49) / 4 = 47.0 thousand dollars.
2. Subtract the mean from each salary to find the differences: 41 - 47 = -6; 46 - 47 = -1; 52 - 47 = 5; 49 - 47 = 2.
3. Square each difference: (-6)^2 = 36; (-1)^2 = 1; (5)^2 = 25; (2)^2 = 4.
4. Calculate the mean of these squared differences: (36 + 1 + 25 + 4) / 4 = 16.5.
5. Finally, take the square root of this value to find the standard deviation: √16.5 ≈ 4.06.

The standard deviation of the salaries is therefore approximately 4.06 thousand dollars, rounded to the nearest hundredth.