The table below summarises the times taken by 50 athletes to run 400 m. Time (t seconds) | 50 ≤ t < 55 | 55 ≤ t < 60 | 60 ≤ t < 65 | 65 < t < 70 | 70 < t < 75 Frequency | 7 | 16 | 15 | 11 | 1 State the modal class.

1. (a)(i)The table below summarises the times taken by 50 athletes to run 400 m. Time (t seconds) | 50 ≤ t < 55 | 55 ≤ t < 60 | 60 ≤ t < 65 | 65 < t < 70 | 70 < t < 75 Frequency | 7 | 16 | 15 | 11 | 1 State the modal class.[1]
2. (a)(ii)Calculate an estimate of the mean time taken by these athletes.[3]
3. (a)(iii)Calculate the probability that an athlete chosen at random took less than 60 seconds to run the 400 m.[2]
4. (b)(i)The cumulative frequency curve summarises the times taken by 80 boys to run 200 m. [Figure of cumulative frequency curve] Find the median time.[1]
5. (b)(ii)Find the interquartile range.[2]
6. (b)(iii)60 girls also ran 200 m. The girl who took the longest time ran 200m in 40 seconds. The girl who took the shortest time ran 200m in 28 seconds. The lower quartile for the boys and the girls is the same. The interquartile range for the girls is 4 seconds. Draw the cumulative frequency curve on the grid above.[3]

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