Question: The masses of a group of 18 Lions were recorded.
10 Lions in Group A had a mean mass of 250kg.
8 Lions in Group B had a mean mass of 198kg.
Calculate the Mean mass of the 18 Lions.
1. **State the problem:** We need to find the mean mass of all 18 lions combined, given the mean masses of two groups.
2. **Formula used:** The mean mass of combined groups is given by
$$\text{Mean}_{total} = \frac{(n_A \times \text{Mean}_A) + (n_B \times \text{Mean}_B)}{n_A + n_B}$$
where $n_A$ and $n_B$ are the number of lions in groups A and B respectively.
3. **Given values:**
- $n_A = 10$, $\text{Mean}_A = 250$
- $n_B = 8$, $\text{Mean}_B = 198$
4. **Calculate total mass:**
$$\text{Total mass} = (10 \times 250) + (8 \times 198) = 2500 + 1584 = 4084$$
5. **Calculate mean mass:**
$$\text{Mean}_{total} = \frac{4084}{10 + 8} = \frac{4084}{18}$$
6. **Simplify the fraction:**
$$\text{Mean}_{total} = \frac{\cancel{4084}}{\cancel{18}} = 226.888\ldots$$
7. **Final answer:** The mean mass of the 18 lions is approximately $226.89$ kg.