(i) To find the median, calculate the cumulative frequency to find the middle value. The cumulative frequencies are: 19, 31, 59, 81, 99, 112. The median is the 56th value, which falls in the 15 < t ≤ 20 interval. The upper quartile (UQ) is the 84th value, which falls in the 25 < t ≤ 40 interval.

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

• 0 < t ≤ 10: fd = 19/10 = 1.9
• 10 < t ≤ 15: fd = 12/5 = 2.4
• 15 < t ≤ 20: fd = 28/5 = 5.6
• 20 < t ≤ 25: fd = 22/5 = 4.4
• 25 < t ≤ 40: fd = 18/15 = 1.2
• 40 < t ≤ 60: fd = 13/20 = 0.65

Draw bars with these heights and corresponding widths.

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

\(\frac{(5 \times 19) + (12.5 \times 12) + (17.5 \times 28) + (22.5 \times 22) + (32.5 \times 18) + (50 \times 13)}{112}\) =\( \frac{2465}{112} = 22.0 \text{ minutes}\)