<div class="content-block"><figure class="question-figure aligncenter" style="text-align: center;"><img src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/public/question-images/pasted/1767944223552-75yqyislj5x.png" style="max-width: min(500px, 100%); height: auto; display: block;" alt="Cumulative frequency graph for Mathematics and Science examinations" class="aligncenter custom-width" /></figure></div>
<p>The cumulative frequency graph shows the distribution of marks for&nbsp;\(400\) students in a Mathematics and Science examination.</p>
<ol class="abc-list"><li><div class="list-item-content"><span class="list-item-text"></span></div><ol class="i-list"><li><div class="list-item-content"><span class="list-item-text">Find the median mark for the Mathematics examination.</span></div></li><li><div class="list-item-content"><span class="list-item-text">Find the interquartile range for the Science examination.</span></div></li><li><div class="list-item-content"><span class="list-item-text">If the distinctions for Mathematics were allocated to the top \(25\%\) of the students, find the mark to achieve a distinction.</span></div></li></ol></li><li><div class="list-item-content"><span class="list-item-text">One student is chosen at random. You may assume that the marks gained in the two examinations are independent. Expressing your answer as a fraction in its lowest terms, calculate the probability that the student gains</span></div><ol class="i-list"><li><div class="list-item-content"><span class="list-item-text">less than \(20\) marks for both examinations,</span></div></li><li><div class="list-item-content"><span class="list-item-text">more than \(60\) marks on one examination, but not on the other.</span></div></li></ol></li></ol>

The cumulative frequency graph shows the distribution of marks for \(400\) students in a Mathematics and Science examination.

Find the median mark for the Mathematics examination.

Find the interquartile range for the Science examination.

If the distinctions for Mathematics were allocated to the top \(25\%\) of the students, find the mark to achieve a distinction.

One student is chosen at random. You may assume that the marks gained in the two examinations are independent. Expressing your answer as a fraction in its lowest terms, calculate the probability that the student gains

Regional Academic Standards: A Comparative Statistical Study

Regional Academic Standards: A Comparative Statistical Study

Video Solution: