(i) To draw the histogram, calculate the frequency density for each class using the formula:

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

Class widths: 5, 5, 10, 20, 40 (in thousands)

Frequency densities: 8, 6, 1.8, 1.7, 0.2

Plot these on the histogram with the horizontal axis labeled 'Capacity (1000s)' and the vertical axis labeled 'Frequency Density'.

(ii) Calculate the mean capacity using the midpoints of each class:

\(\text{Mean} = \frac{(5 \times 40) + (10 \times 30) + (17.5 \times 18) + (32.5 \times 34) + (62.5 \times 8)}{130}\)

\(= \frac{2420}{130} = 18.6 \text{ thousand}\)

(iii) To find the median and lower quartile groups:

Median position: \(\frac{130 + 1}{2} = 65.5\)

Lower quartile position: \(\frac{130 + 1}{4} = 32.75\)

The median group is 8000–12000 and the lower quartile group is 3000–7000.