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 (average) of the data set: Mean = \( \frac{(6 + 11 + 11 + 19)}{4} = \frac{47}{4} = 11.75 \) Next, find the squared differences from the mean: 1. \( (6 - 11.75)^2 = (-5.75)^2 = 33.0625 \) 2. \( (11 - 11.75)^2 = (-0.75)^2 = 0.5625 \) 3. \( (11 - 11.75)^2 = (-0.75)^2 = 0.5625 \) 4. \( (19 - 11.75)^2 = (7.25)^2 = 52.5625 \) Now, sum these squared differences: \( 33.0625 + 0.5625 + 0.5625 + 52.5625 = 86.75 \) Next, divide by the number of data items minus one (N-1) for sample standard deviation: Variance = \( \frac{86.75}{4 - 1} = \frac{86.75}{3} \approx 28.9167 \) Finally, take the square root of the variance to find the standard deviation: Standard Deviation = \( \sqrt{28.9167} \approx 5.38 \) So, the standard deviation is approximately **5.38** (rounded to two decimal places).