Mean Spending
1. **State the problem:** We have data for boys' spending grouped in class intervals with frequencies and need to estimate the boys' mean spending first.
2. **Identify midpoints:** The midpoints are missing, so we calculate them:
- For 0 ≤ x < 20, midpoint = $\frac{0+20}{2} = 10$
- For 20 ≤ x < 40, midpoint = $\frac{20+40}{2} = 30$
- For 40 ≤ x < 60, midpoint = $\frac{40+60}{2} = 50$
- For 60 ≤ x < 80, midpoint = $\frac{60+80}{2} = 70$
3. **Calculate the mean for boys:** Using the formula for grouped data mean:
$$ \text{Mean} = \frac{\sum (\text{midpoint} \times \text{frequency})}{\sum \text{frequency}} $$
Calculate the numerator:
$$ (10 \times 22) + (30 \times 9) + (50 \times 6) + (70 \times 3) = 220 + 270 + 300 + 210 = 1000 $$
Sum of frequencies is 40.
So,
$$ \text{Mean}_{boys} = \frac{1000}{40} = 25 $$
4. **Given:** Mean for girls is 35.
5. **Calculate the girls' mean as a percentage of the boys' mean:**
$$ \frac{35}{25} \times 100 = 140\% $$
**Final answer:** Girls' mean spending is 140% of boys' mean spending.