72 students each took a theory test followed by a practical test - OCR - GCSE Maths - Question 8 - 2017 - Paper 1

To complete the frequency tree, we first need to find out how many students passed the theory test. Since 5/6 of the 72 students passed, we calculate:

$\frac{5}{6} \times 72 = 60$

This means 60 students passed the theory test. Since there are 72 students in total, the number of students who failed the theory test is:

$72 - 60 = 12$

Now, we will place this information in the frequency tree:

• Passed Theory Test (60): Out of these, 52 passed the practical test (as given) and 8 failed (i.e., $60 - 52 = 8$).
• Failed Theory Test (12): All of these failed the practical test.

The completed frequency tree will show:

• Passed Theory Test: 60
  • Passed Practical Test: 52
  • Failed Practical Test: 8
• Failed Theory Test: 12 (Failed Practical Test: 12).

The practical test was passed by more students because:

• 52 students passed the practical test (after having passed the theory test), and there are 0 more who could pass since those in the failed theory group also failed the practical. In contrast, 60 students passed the theory test overall.
• However, if we analyze students who passed each separately, the total of students who passed the practical test includes students who also passed the theory, leading to a direct comparison of counts.
• Thus, we see that the total number of students passing the practical test is lower than those passing the theory test, but since the question asks if more passed practical, we can conclude with the count as we see:

Practical: 52 students Theory: 60 students

Therefore, more students passed the theory test compared to the practical test.