The following are some particulars of the distribution of weights of boys and girls in a class:   Boys Girls Number 100 50 Mean 60kg 45kg Variance 9 4 Which of the distributions is more variable?

Explanation

To determine which of the distributions (boys or girls) is more variable, we can use the concept of the coefficient of variation (CV). The coefficient of variation is a standardized measure of dispersion of a probability distribution or frequency distribution. It is calculated as the ratio of the standard deviation to the mean, expressed as a percentage.

### Step-by-Step Solution:

1. **Identify Given Data:**
- For Boys:
- Number of boys (n_B) = 100
- Mean weight (X̄_B) = 60 kg
- Variance (σ²_B) = 9
- For Girls:
- Number of girls (n_G) = 50
- Mean weight (X̄_G) = 45 kg
- Variance (σ²_G) = 4

2. **Calculate Standard Deviation:**
- The standard deviation (σ) is the square root of the variance.
- For Boys:
\[ σ_B = \sqrt{σ²_B} = \sqrt{9} = 3 \text{ kg} \]
- For Girls:
\[ σ_G = \sqrt{σ²_G} = \sqrt{4} = 2 \text{ kg} \]

3. **Calculate Coefficient of Variation (CV):**
- The formula for the coefficient of variation is:
\[ CV = \left(\frac{σ}{X̄}\right) \times 100\% \]
- For Boys:
\[ CV_B = \left(\frac{σ_B}{X̄_B}\right) \times 100 = \left(\frac{3}{60}\right) \times 100 = 5\% \]
- For Girls:
\[ CV_G = \left(\frac{σ_G}{X̄_G}\right) \times 100 = \left(\frac{2}{45}\right) \times 100 \approx 4.44\% \]

4. **Compare Coefficients of Variation:**
- From the calculations:
- CV_B = 5%
- CV_G ≈ 4.44%
- Since 5% > 4.44%, the boys' distribution is more variable than the girls' distribution.

### Conclusion:
The weights of boys are more variable compared to the weights of girls in the class.