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The box-and-whisker diagram below shows the distribution of the times taken by a large group of students of an athletic club to finisha 100m _ race: a 121 132 b ig. Time () The inter-quartile range and the range of the distribution are 3.25 and 6.8s respectively. (a) Find @ and b. (b) The students join a training program. It is found that the longest time taken by the students to finish a 100m _ race after the training is 2.9s less than that before the training. The trainer claims that at least 25% of the students show improvement in the time taken to finish a 100m race after the training. Do you agree? Explain your answer. (4 marks) The bar chart below shows the distribution of the numbers of family members of the employees of company D, Distribution of the numbers of family members of the employees of company D 24 LJ °o a > Number of employees S oS RS ‘Number of family members (a) Find the mean, the inter-quartile range and the standard deviation of the above distribution. (b) Anemployee leaves company D. The number of family members of this employee is 7. Find the change in the standard deviation of the numbers of family members of the employees of company D due to the leaving of this employee. (5 marks) There are 33 paintings in an art gallery. The box-and-whisker diagram below shows the distribution of the prices (in thousand dollars) of the paintings in the art gallery. It is given that the mean of this distribution is 53 thousand dollars. i H i Price (thousand dollars) 18 42 55 63 (a) Find the range and the inter-quartile range of the above distribution. (3 marks) (b) Four paintings of respective prices (in thousand dollars) 32, 34, 58 and 59 are now donated toa museum. Find the mean and the median of the prices of the remaining paintings in the art gallery. (3 marks) The bar chart below shows the distribution of the ages of the children in a group, where a>I1 and 4
