1. **State the problem:** We are given a data set and need to calculate the mean and standard deviation. 2. **Calculate the mean ($\bar{x}$):** The mean is the sum of all data values divided by the number of values. Given data: 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 Number of data points $n = 30$ Sum of data values $= 1527$ Mean: $$\bar{x} = \frac{\sum x_i}{n} = \frac{1527}{30} = 50.9$$ 3. **Calculate the standard deviation ($s$):** The formula for sample standard deviation is $$s = \sqrt{\frac{1}{n-1} \sum_{i=1}^n (x_i - \bar{x})^2}$$ 4. **Calculate each squared deviation $(x_i - \bar{x})^2$ and sum them:** For example, for $x_1=21$: $$ (21 - 50.9)^2 = (-29.9)^2 = 894.01 $$ Calculate all and sum: $$\sum (x_i - \bar{x})^2 = 11094.3$$ 5. **Calculate $s$:** $$s = \sqrt{\frac{11094.3}{30-1}} = \sqrt{\frac{11094.3}{29}} = \sqrt{382.56} = 19.56$$ **Final answers:** - Mean $\bar{x} = 50.9$ - Standard deviation $s = 19.56$ (rounded to two decimal places)