(i) To find \(a\) and \(b\):

\(a = 422 + 72 = 494\)

\(b = 540 - 494 = 46\)

(ii) Draw a cumulative frequency graph using the points: (10, 210), (20, 344), (30, 422), (40, 494), (60, 540).

(iii) The median is found by locating the 270th person on the cumulative frequency graph, which corresponds to approximately 13.5 to 14.6 minutes.

(iv) Calculate the mean \(m\) using midpoints:

\(m = \frac{(5 \times 210 + 15 \times 134 + 25 \times 78 + 35 \times 72 + 50 \times 46)}{540} = \frac{9830}{540} = 18.2\) minutes

Calculate the standard deviation \(s\):

\(s = \sqrt{\frac{(5^2 \times 210 + 15^2 \times 134 + 25^2 \times 78 + 35^2 \times 72 + 50^2 \times 46)}{540} - 18.2^2} = 14.2\) minutes

(v) Calculate the range \((m - \frac{1}{2}s)\) to \((m + \frac{1}{2}s)\):

\(18.2 \pm 7.1 = 11.1, 25.3\)

From the cumulative frequency graph, estimate the number of people between these times: 390 - 225 = 155 to 170 people.