Find the standard deviation for the following group of data items. $$ 29,32,32,38 $$ The standard deviation is approximately (Round to two decimal places as needed.)

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To calculate the standard deviation for the data set $$ 29, 32, 32, 38 $$, we can follow these steps:

1. **Calculate the mean (average)**:
   $$
   \text{Mean} = \frac{\text{Sum of all data items}}{\text{Number of data items}} = \frac{29 + 32 + 32 + 38}{4} = \frac{131}{4} = 32.75
   $$

2. **Calculate the squared differences from the mean**:
   $$
   (29 - 32.75)^2 = (-3.75)^2 = 14.0625
   $$
   $$
   (32 - 32.75)^2 = (-0.75)^2 = 0.5625
   $$
   $$
   (32 - 32.75)^2 = (-0.75)^2 = 0.5625
   $$
   $$
   (38 - 32.75)^2 = (5.25)^2 = 27.5625
   $$

3. **Sum the squared differences**:
   $$
   \text{Sum of squared differences} = 14.0625 + 0.5625 + 0.5625 + 27.5625 = 42.75
   $$

4. **Calculate the variance**:
   Since we have a sample of the population, we will use $$ n - 1 $$ (where $$ n $$ is the number of data items) for the calculation of variance:
   $$
   \text{Variance} = \frac{\text{Sum of squared differences}}{n - 1} = \frac{42.75}{4 - 1} = \frac{42.75}{3} = 14.25
   $$

5. **Calculate the standard deviation**:
   $$
   \text{Standard deviation} = \sqrt{\text{Variance}} = \sqrt{14.25} \approx 3.77
   $$

Thus, the standard deviation of the data set $$ 29, 32, 32, 38 $$ is approximately $$ \boxed{3.77} $$.
The standard deviation of the data set $$ 29, 32, 32, 38 $$ is approximately 3.77.

Find the standard deviation for the following group of data items. \[ 29,32,32,38 \] The standard deviation is approximately (Round to two decimal places as needed.)

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