Find the standard deviation of the numbers 3,6,2,1,7 and 5.

Answer Details

To find the standard deviation of a set of numbers, we need to follow these steps: 1. Find the mean (average) of the numbers. 2. For each number, subtract the mean and square the result. 3. Find the mean of the squared differences. 4. Take the square root of the mean to get the standard deviation. So, let's apply these steps to the given set of numbers: 3, 6, 2, 1, 7, 5. 1. The mean is (3 + 6 + 2 + 1 + 7 + 5) / 6 = 4. 2. For each number, subtract the mean and square the result: \begin{align*} (3 - 4)^2 &= 1 \\ (6 - 4)^2 &= 4 \\ (2 - 4)^2 &= 4 \\ (1 - 4)^2 &= 9 \\ (7 - 4)^2 &= 9 \\ (5 - 4)^2 &= 1 \end{align*} 3. Find the mean of the squared differences: \begin{align*} \frac{1 + 4 + 4 + 9 + 9 + 1}{6} &= \frac{28}{6} \\ &= 4.67 \end{align*} 4. Take the square root of the mean to get the standard deviation: \begin{align*} \sqrt{4.67} &\approx 2.16 \end{align*} Therefore, the standard deviation of the given set of numbers is approximately 2.16. So, the correct answer is (b) 2.16.