1. **State the problem:** Calculate the mean for the given frequency tables without using a calculator. 2. **Formula for mean of frequency distribution:** $$\text{Mean} = \frac{\sum (x \times f)}{\sum f}$$ where $x$ is the value and $f$ is the frequency. 3. **First table (Age):** Values: 5, 6, 7, 8 Frequencies: 2, 2, 5, 1 Total frequency $\sum f = 2 + 2 + 5 + 1 = 10$ Calculate $\sum (x \times f)$: $$5 \times 2 = 10$$ $$6 \times 2 = 12$$ $$7 \times 5 = 35$$ $$8 \times 1 = 8$$ Sum: $$10 + 12 + 35 + 8 = 65$$ Mean: $$\frac{65}{10} = 6.5$$ 4. **Second table (Number of phones):** Values: 0, 1, 2, 3, 4, 5 Frequencies: 1, 3, 2, 0, 4, 0 Total frequency $\sum f = 1 + 3 + 2 + 0 + 4 + 0 = 10$ Calculate $\sum (x \times f)$: $$0 \times 1 = 0$$ $$1 \times 3 = 3$$ $$2 \times 2 = 4$$ $$3 \times 0 = 0$$ $$4 \times 4 = 16$$ $$5 \times 0 = 0$$ Sum: $$0 + 3 + 4 + 0 + 16 + 0 = 23$$ Mean: $$\frac{23}{10} = 2.3$$ 5. **Third table (Level):** Values: 3, 4, 5, 6, 7 Frequencies: 1, 9, 7, 2, 1 Total frequency $\sum f = 1 + 9 + 7 + 2 + 1 = 20$ Calculate $\sum (x \times f)$: $$3 \times 1 = 3$$ $$4 \times 9 = 36$$ $$5 \times 7 = 35$$ $$6 \times 2 = 12$$ $$7 \times 1 = 7$$ Sum: $$3 + 36 + 35 + 12 + 7 = 93$$ Mean: $$\frac{93}{20} = 4.65$$ **Final answers:** - Mean age = 6.5 - Mean number of phones = 2.3 - Mean level = 4.65