1. **State the problem:** Find the mean, median, and standard deviation of the data set: 12, 15, 18, 20, 22, 25, 28. 2. **Mean:** The mean is the average of the numbers. Use the formula: $$\text{Mean} = \frac{\sum x_i}{n}$$ where $x_i$ are the data points and $n$ is the number of data points. Calculate the sum: $$12 + 15 + 18 + 20 + 22 + 25 + 28 = 140$$ Number of data points $n = 7$. Calculate the mean: $$\text{Mean} = \frac{140}{7} = 20$$ 3. **Median:** The median is the middle value when the data is ordered. The data in order is already: 12, 15, 18, 20, 22, 25, 28. Since $n=7$ (odd), the median is the middle value, which is the 4th value: $$\text{Median} = 20$$ 4. **Standard deviation:** Measures the spread of data around the mean. Use the formula for sample standard deviation: $$s = \sqrt{\frac{1}{n-1} \sum_{i=1}^n (x_i - \bar{x})^2}$$ where $\bar{x}$ is the mean. Calculate each squared deviation: $$(12-20)^2 = 64$$ $$(15-20)^2 = 25$$ $$(18-20)^2 = 4$$ $$(20-20)^2 = 0$$ $$(22-20)^2 = 4$$ $$(25-20)^2 = 25$$ $$(28-20)^2 = 64$$ Sum of squared deviations: $$64 + 25 + 4 + 0 + 4 + 25 + 64 = 186$$ Divide by $n-1=6$: $$\frac{186}{6} = 31$$ Take the square root: $$s = \sqrt{31} \approx 5.57$$ **Final answers:** - Mean = 20 - Median = 20 - Standard deviation $\approx 5.57$