1. **State the problem:** We are given a sample data set and need to calculate the mean $\bar{x}$ and standard deviation $s$. 2. **Recall formulas:** - Mean: $$\bar{x} = \frac{1}{n} \sum_{i=1}^n x_i$$ - Sample standard deviation: $$s = \sqrt{\frac{1}{n-1} \sum_{i=1}^n (x_i - \bar{x})^2}$$ 3. **Calculate the mean:** Sum all data values: $$21 + 48 + 24 + 38 + 36 + 80 + 33 + 51 + 77 + 35 + 79 + 32 + 50 + 90 + 41 + 12 + 50 + 43 + 64 + 48 + 71 + 74 + 88 + 49 + 91 + 44 + 57 + 24 + 11 + 66 = 1527$$ Count of data values $n = 30$ Calculate mean: $$\bar{x} = \frac{1527}{30} = 50.9$$ 4. **Calculate the standard deviation:** Calculate each squared deviation $(x_i - \bar{x})^2$ and sum: $$\sum (x_i - 50.9)^2 = 10288.3$$ Apply formula: $$s = \sqrt{\frac{10288.3}{30 - 1}} = \sqrt{354.77} = 18.83$$ **Final answers:** - Mean $\bar{x} = 50.9$ - Standard deviation $s = 18.83$ (rounded to two decimal places)