1. **State the problem:** We are given the ages (in months) at which eight children first walked: 12, 11, 16, 19, 10, 12, 12, 13. We need to calculate the mean and standard deviation of this data. 2. **Calculate the mean:** The mean (average) is given by the formula: $$\text{mean} = \frac{\sum x_i}{n}$$ where $x_i$ are the data points and $n$ is the number of data points. Sum the data: $$12 + 11 + 16 + 19 + 10 + 12 + 12 + 13 = 105$$ Number of data points: $$n = 8$$ Calculate the mean: $$\text{mean} = \frac{105}{8} = 13.125$$ 3. **Calculate the standard deviation:** The standard deviation $s$ for a sample is given by: $$s = \sqrt{\frac{1}{n-1} \sum_{i=1}^n (x_i - \bar{x})^2}$$ where $\bar{x}$ is the mean. Calculate each squared deviation: $$(12 - 13.125)^2 = (-1.125)^2 = 1.265625$$ $$(11 - 13.125)^2 = (-2.125)^2 = 4.515625$$ $$(16 - 13.125)^2 = 2.875^2 = 8.265625$$ $$(19 - 13.125)^2 = 5.875^2 = 34.515625$$ $$(10 - 13.125)^2 = (-3.125)^2 = 9.765625$$ $$(12 - 13.125)^2 = 1.265625$$ $$(12 - 13.125)^2 = 1.265625$$ $$(13 - 13.125)^2 = (-0.125)^2 = 0.015625$$ Sum of squared deviations: $$1.265625 + 4.515625 + 8.265625 + 34.515625 + 9.765625 + 1.265625 + 1.265625 + 0.015625 = 60.875$$ Divide by $n-1=7$: $$\frac{60.875}{7} = 8.696428571$$ Take the square root: $$s = \sqrt{8.696428571} \approx 2.949$$ **Final answers:** - Mean age: $13.125$ months - Standard deviation: approximately $2.949$ months