The standard deviation of the numbers \( 2,3,4,4 \), and 6 is approximately (Round to three decimal places as needed.)

To find the standard deviation of the given numbers, we can use the formula for the standard deviation of a set of numbers: \[ \sigma = \sqrt{\frac{\sum_{i=1}^{n} (x_i - \mu)^2}{n}} \] where: - \( \sigma \) is the standard deviation - \( x_i \) are the individual numbers - \( \mu \) is the mean of the numbers - \( n \) is the total number of values First, let's calculate the mean of the given numbers: \[ \mu = \frac{2 + 3 + 4 + 4 + 6}{5} = \frac{19}{5} = 3.8 \] Next, we calculate the squared differences from the mean for each number: \[ (2 - 3.8)^2 = (-1.8)^2 = 3.24 \] \[ (3 - 3.8)^2 = (-0.8)^2 = 0.64 \] \[ (4 - 3.8)^2 = (0.2)^2 = 0.04 \] \[ (4 - 3.8)^2 = (0.2)^2 = 0.04 \] \[ (6 - 3.8)^2 = (2.2)^2 = 4.84 \] Now, we sum these squared differences: \[ 3.24 + 0.64 + 0.04 + 0.04 + 4.84 = 8.8 \] Finally, we divide the sum by the total number of values to find the standard deviation: \[ \sigma = \sqrt{\frac{8.8}{5}} = \sqrt{1.76} \approx 1.326 \] Therefore, the standard deviation of the numbers 2, 3, 4, 4, and 6 is approximately 1.326.