1. The problem asks for the mean check-in weight of 30 passengers given a frequency table of weights. 2. The formula for the mean when data is grouped with frequencies is: $$\text{Mean} = \frac{\sum (\text{weight} \times \text{frequency})}{\sum \text{frequency}}$$ 3. Calculate the total sum of weights multiplied by their frequencies: $$16 \times 4 = 64$$ $$17 \times 4 = 68$$ $$18 \times 6 = 108$$ $$19 \times 6 = 114$$ $$20 \times 4 = 80$$ $$21 \times 3 = 63$$ $$22 \times 3 = 66$$ 4. Sum these products: $$64 + 68 + 108 + 114 + 80 + 63 + 66 = 563$$ 5. Sum the frequencies: $$4 + 4 + 6 + 6 + 4 + 3 + 3 = 30$$ 6. Calculate the mean: $$\text{Mean} = \frac{563}{30} = 18.77$$ 7. Therefore, the mean check-in weight is 18.77 kilograms.