(i) The frequency density for the 1 – 10 interval is given by:

\(\text{Frequency Density} = \frac{\text{Frequency}}{\text{Class Width}} = \frac{2x}{10}\)

We know the height is 3 cm, so:

\(3 = \frac{2x}{10}\)

Solving for \(x\):

\(3 \times 10 = 2x\)

\(30 = 2x\)

\(x = 15\)

For the 51 – 70 interval, the class width is 20, and the frequency is \(x = 15\).

\(\text{Frequency Density} = \frac{15}{20} = 0.75\)

Thus, the height of the 51 – 70 rectangle is 0.75 cm.

(ii) To estimate the mean weight, use the midpoints of each interval:

\(\text{Mean} = \frac{(5.5 \times 30) + (15.5 \times 60) + (23 \times 45) + (28 \times 75) + (40.5 \times 60) + (60.5 \times 15)}{285}\)

\(= \frac{165 + 930 + 1035 + 2100 + 2430 + 907.5}{285}\)

\(= \frac{7567.5}{285}\)

\(\approx 26.6 \text{ grams}\)