Final answer:
To find the standard deviation of the insurance rates, calculate the mean, subtract the mean from each individual rate, square the differences, find the average of the squared differences, and take the square root of the average. The standard deviation is approximately $13.42.
Step-by-step explanation:
To calculate the standard deviation of a set of numbers, you can use the formula:
Step 1: Find the mean of the set of numbers. In this case, the mean is obtained by adding up all the insurance rates and dividing by the total number of rates, which is 4. The mean is (202 + 168 + 207 + 172) / 4 = 749 / 4 = 187.25.
Step 2: Subtract the mean from each individual rate and square the result. The squared differences are 14.25^2, -19.25^2, 19.75^2, and -15.25^2.
Step 3: Find the average of the squared differences. In this case, the average is (14.25^2 + (-19.25)^2 + 19.75^2 + (-15.25)^2) / 4 = 719.875 / 4 = 179.96875.
Step 4: Take the square root of the average to find the standard deviation. √179.96875 ≈ 13.42.
Therefore, the standard deviation of the insurance rates is approximately $13.42.