4 The table shows information about the heights of 80 children. Height 1.2 1 h G 1.4 1.4 1 h G 1.5 1.5 1 h G 1.65 1.65 1 h G 1.8 1.8 1 h G 1.9 (h metres) Frequency 2 13 24 32 9 (a) (i) Write down the interval containing the median. .................... 1 h G .................... [1] (ii) Calculate an estimate of the mean height. ............................................. m [4] (b) (i) One of these children is chosen at random. Calculate the probability that they have a height of 1.4 m or less. ................................................. [1] (ii) Two of these children are chosen at random. Calculate the probability that both children are taller than 1.5 m but only one of them is taller than 1.8 m. ................................................. [3] © UCLES 2023 0580/42/M/J/23 9 (c) (i) Complete the cumulative frequency table for the heights. Height h G 1.4 h G 1.5 h G 1.65 h G 1.8 h G 1.9 (h metres) Cumulative 2 frequency [2] (ii) On the grid, draw the cumulative frequency diagram. 80 70 60 50 Cumulative 40 frequency 30 20 10 0 h 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 Height (m) [3] (d) Use your diagram to find an estimate of (i) the interquartile range ..............................................m [2] (ii) the 60th percentile. ............................................ m [2] © UCLES 2023 0580/42/M/J/23 [Turn over 10