1. **Problem Statement:** Understand the formulas for Arithmetic Mean (AM) and Weighted Arithmetic Mean (WAM) and solve related problems. 2. **Formulas:** - Arithmetic Mean (AM) is given by $$AM = \frac{\sum x_i}{n}$$ where $x_i$ are the data points and $n$ is the number of data points. - Weighted Arithmetic Mean (WAM) is given by $$WAM = \frac{\sum w_i x_i}{\sum w_i}$$ where $w_i$ are the weights corresponding to each data point $x_i$. 3. **Explanation:** - Arithmetic Mean is the simple average of all values. - Weighted Arithmetic Mean accounts for different importance (weights) of each value. 4. **Example Question 1:** Find the Arithmetic Mean of the numbers 5, 8, 12, 20. 5. **Solution:** - Calculate sum: $5 + 8 + 12 + 20 = 45$ - Number of data points: $4$ - Apply formula: $$AM = \frac{45}{4} = 11.25$$ 6. **Example Question 2:** Find the Weighted Arithmetic Mean of marks 80, 90, 70 with weights 2, 3, 1 respectively. 7. **Solution:** - Calculate weighted sum: $80 \times 2 + 90 \times 3 + 70 \times 1 = 160 + 270 + 70 = 500$ - Sum of weights: $2 + 3 + 1 = 6$ - Apply formula: $$WAM = \frac{500}{6} \approx 83.33$$ These formulas and examples are fundamental for BCA Semester topics on Measures of Central Tendency.