Find the standard deviation for the following group of data items. \( 6,11,11,19 \) The standard deviation is approximately (Round to two decimal places as needed.)

To calculate the standard deviation, first find the mean: \[ \text{Mean} = \frac{6 + 11 + 11 + 19}{4} = \frac{47}{4} = 11.75 \] Next, calculate the squared differences from the mean: \[ (6 - 11.75)^2 = (-5.75)^2 = 33.0625 \] \[ (11 - 11.75)^2 = (-0.75)^2 = 0.5625 \] \[ (11 - 11.75)^2 = (-0.75)^2 = 0.5625 \] \[ (19 - 11.75)^2 = (7.25)^2 = 52.5625 \] Now sum these squared differences: \[ 33.0625 + 0.5625 + 0.5625 + 52.5625 = 86.75 \] To find the variance, divide by the number of data items (n = 4): \[ \text{Variance} = \frac{86.75}{4} = 21.6875 \] Finally, the standard deviation is the square root of the variance: \[ \text{Standard Deviation} \approx \sqrt{21.6875} \approx 4.65 \] So, the standard deviation is approximately \(4.65\) (rounded to two decimal places).