Unit 7 Averages and range 6 Problem-solving This back-to-back stem and leaf diagram shows the heights, in cm, of Class 11W students. Boys Girls Q6 hint Compare an 15 7 7 average and the range. 7 16 2 3 6 7 8 9 9 9 8 7 5 2 0 17 0 1 2 8 9 5 4 3 2 1 1 0 18 3 3 19 Key For the boys: 7|16 means a height of 167 cm For the girls: 15|7 means a height of 157 cm Compare the distribution of heights of the boys with the distribution of heights of the girls. 7 Exam-style question A rugby team played six games. Here are the number of points they scored in each game. 24 8 18 6 12 19 a Work out the median score for these six games. (2 marks) b Work out the mean score for these six games. (2 marks) The rugby team played one more game. The mean score for all seven games is 16. c Work out the number of points the team scored in the seventh game. (2 marks) March 2012, Q15, 1380/2F 8 This table gives information about the prices of cars at a car supermarket. a Work out an estimate of the mean price. b Which is the modal class? c Which class contains the median? d Work out an estimate of the range. n Q8c hint When n is large, use __ to give the 2 position of the median. Problem-solving The histogram shows the distribution of times for an Austrian downhill ski race. a Work out an estimate of the mean time. b Work out an estimate of the range. Q9a hint Make a frequency table for these times. Price, p (£) Frequency 7000 , p < 8000 652 8000 , p < 9000 583 9000 , p < 12000 976 12000 , p < 15000 354 15000 , p < 20000 185 25 20 Frequency 9 Exam hint In part c first work out the total number of points scored in the 7 games. 15 10 5 0 2:02 2:04 2:06 2:08 Time (mins:secs) 2:10 10 1200 people attend a concert. The organisers would like some feedback from members of the audience to help them plan their next event. They decide to sample 15% of the audience. a How many people should they include in their sample? b How could they select a representative sample? 204