Median Percentage Marks Calculation

To find the median percentage marks, we first need to determine the marks of all students who appeared for the examination.

1. Identify Student Marks

• Total students appeared: 9
• Number of students who failed: 4
• Number of students who passed: $9 - 4 = 5$
• Marks of the passed students: 80%, 55%, 52%, 66%, 81%
• Passing criteria: 40%
• Assuming the 4 failed students scored the minimum passing mark (40%), their marks are 40%, 40%, 40%, 40%.

2. Compile and Sort All Marks

Combine the marks of failed and passed students and sort them in ascending order:

Marks List: {40%, 40%, 40%, 40%, 52%, 55%, 66%, 80%, 81%}

The list contains 9 values ($n=9$) and is already sorted.

3. Calculate Median

The median is the middle value in a sorted dataset. For an odd number of data points, the median position is calculated using the formula:

Median Position = $\frac{n+1}{2}$

Substituting $n=9$:

Median Position = $\frac{9+1}{2} = \frac{10}{2} = 5$

The median is the 5th value in the sorted list.

The 5th value in the sorted list {40%, 40%, 40%, 40%, 52%, 55%, 66%, 80%, 81%} is 52%.

Therefore, the median of the percentage marks is 52%.