Mathematics 4024 · O Level · Cumulative frequency diagrams

Cumulative frequency diagrams — practice question

The cumulative frequency graph displays the marks scored by 80 students in a Maths test.
(a(i))[1]

Use the diagram to estimate the median.

(a(ii))[2]

A total of $60\%$ of the students passed the test. Use the diagram to determine how many marks were needed to pass.

(a(iii))[2]

Using the information shown on the diagram, complete the frequency table.

(b)[5]

The times taken by the 80 students to finish a Science test are displayed in the frequency table. The estimated mean time to complete the test is $67.625$ minutes. This is found by using the mid-interval value as an estimate of the time in each class interval. Calculate the value of $p$ and the value of $q$.

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