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 determine if we're treating these data as the entire population or just a sample. Since the problem refers to “the following group of data items” without specifying that it is a sample, we will assume that these four numbers constitute the entire population. Step 1. Find the mean.   Mean = (6 + 11 + 11 + 19) / 4 = 47 / 4 = 11.75 Step 2. Find the squared difference of each data item from the mean.   For 6:  (6 − 11.75)² = (−5.75)² = 33.0625   For 11: (11 − 11.75)² = (−0.75)² = 0.5625   For 11: (11 − 11.75)² = (−0.75)² = 0.5625   For 19: (19 − 11.75)² = (7.25)² = 52.5625 Step 3. Find the variance by dividing the sum of these squared differences by the number of data items.   Sum of squared differences = 33.0625 + 0.5625 + 0.5625 + 52.5625 = 86.75   Variance = 86.75 / 4 = 21.6875 Step 4. Take the square root of the variance to obtain the standard deviation.   Standard deviation = √21.6875 ≈ 4.66 Thus, the standard deviation for the data items is approximately 4.66.