1. **State the problem:** We have 70 numbers with different values and frequencies: 15 numbers are 60, 10 numbers are 75, 12 numbers are 55, 9 numbers are 65, and the rest are 80. We need to find the mean of these numbers. 2. **Formula for mean:** The mean is given by $$\text{Mean} = \frac{\text{Sum of all values}}{\text{Total number of values}}$$ 3. **Calculate the number of 80s:** Total numbers = 70 Sum of known frequencies = 15 + 10 + 12 + 9 = 46 Number of 80s = 70 - 46 = 24 4. **Calculate the sum of all values:** $$\text{Sum} = 15 \times 60 + 10 \times 75 + 12 \times 55 + 9 \times 65 + 24 \times 80$$ Calculate each term: $$15 \times 60 = 900$$ $$10 \times 75 = 750$$ $$12 \times 55 = 660$$ $$9 \times 65 = 585$$ $$24 \times 80 = 1920$$ Sum all: $$900 + 750 + 660 + 585 + 1920 = 4815$$ 5. **Calculate the mean:** $$\text{Mean} = \frac{4815}{70}$$ Simplify the fraction: $$\frac{\cancel{4815}^{69} \times 70}{\cancel{70}} = 68.7857$$ (approx) 6. **Final answer:** The mean of the numbers is approximately **68.79**.