A group of 80 students enters a science quiz. The table shows the distribution of their scores. Score (s) | 0<s≤10 | 10<s≤20 | 20<s≤30 | 30<s≤40 | 40<s≤50 | 50<s≤60 Frequency | 4 | 12 | 16 | 23 | 20 | 5

1. (a)Calculate an estimate of the mean score.[3]
2. (b)(i)Complete the cumulative frequency table for their scores. Score (s) | s ≤ 10 | s ≤ 20 | s ≤ 30 | S ≤ 40 | s ≤ 50 | s ≤ 60 Cumulative frequency | 4 | | | | | 80[1]
3. (b)(ii)On the grid below, draw a horizontal s-axis for 0 ≤ s ≤ 60 using a scale of 2 cm to represent 10 points and a vertical axis from 0 to 80 using a scale of 2 cm to represent 20 students. Draw a smooth cumulative frequency curve to represent this information. [Grid][3]
4. (b)(iii)(a)Use your graph to estimate the median score,[1]
5. (b)(iii)(b)the interquartile range of the scores.[2]
6. (c)Students who scored more than 40 points can enter the next round of the quiz. Two of these students are selected at random. Work out the probability that both students scored more than 50 points.[2]

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