A company asked their employees how long they took to travel to work one day. The table summarises the times for 120 employees. Time (t minutes) | 0 < t ≤ 20 | 20 < t ≤ 40 | 40 < t ≤ 60 | 60 < t ≤ 80 | 80 < t ≤ 100 -------------|------------|-------------|-------------|-------------|------------- Frequency | 12 | 28 | 45 | 22 | 13 [Grid for cumulative frequency curve]

1. (a)(i)Complete the cumulative frequency table below. Time (t minutes) | t ≤ 0 | t ≤ 20 | t ≤ 40 | t ≤ 60 | t ≤ 80 | t ≤ 100 ----------------|-------|--------|--------|--------|--------|----------- Cumulative frequency | 0 | | | | | 120[1]
2. (a)(ii)On the grid, draw a smooth cumulative frequency curve to represent these results.[2]
3. (b)(i)Use your curve to estimate the median time,[1]
4. (b)(ii)Use your curve to estimate the interquartile range of the times.[2]
5. (c)Calculate an estimate of the mean time taken for the employees to travel to work.[3]

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