### Box-and-whisker analysis

Question Sample Titled 'Box-and-whisker analysis'

The box-and-whisker diagram below shows the distribution of the score deduction by mistakes received by a group of students of a class in a Mathematics exam:

${21.7}$${35.4}$${29.4}$${24.3}$${b}$Score deduction($\text{mark}$)

 The inter-quartile range of the distribution is ${7.7}$ $\text{marks}$ . (a) Find ${b}$ . (b) The students join a remedial class. It is found that the highest score deduction by mistakes received by the students in a Mathematics exam after the remedial class is ${4.7}$ $\text{marks}$ less than that before the remedial class. The manager of the remedial class claims that at least 25% of the students show improvement in the score deduction by mistakes received in a Mathematics exam after the remedial class. Do you agree? Explain your answer.  (3 marks)

 (a) ${b}$ $={24.3}+{7.7}$  $={32}$ 1A (b) The highest score deduction by mistakes received by the students in a Mathematics exam after the remedial class   $={35.4}-{4.7}$  $={30.7}$ which is less than the upper quartile of the distribution of the score deduction by mistakes received before the remedial class. 1M Thus, the claim is agreed. 1A

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