(i) To find the lower quartile, we need to determine the position of the 25th percentile in the cumulative frequency distribution. The cumulative frequencies are:

- 10–14: 6

\(- 15–19: 6 + 12 = 18\)

\(- 20–24: 18 + 14 = 32\)

\(- 25–34: 32 + 10 = 42\)

\(- 35–59: 42 + 8 = 50\)

The 25th percentile corresponds to the 12.5th value. Since the cumulative frequency reaches 18 in the 15–19 interval, the lower quartile is in the 15–19 kg class interval.

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

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

- 10–14: \(\frac{6}{5} = 1.2\)

- 15–19: \(\frac{12}{5} = 2.4\)

- 20–24: \(\frac{14}{5} = 2.8\)

- 25–34: \(\frac{10}{10} = 1.0\)

- 35–59: \(\frac{8}{25} = 0.32\)

Draw bars with these heights on the histogram, ensuring the horizontal axis ranges from at least 9.5 to 59.5 and the vertical axis is labeled with frequency density.