Question 4

Explanation

To determine the passing percentage, we must check two passing conditions for each student:

1. The Science score must be higher than the median Science score of all students.
2. The average exam score (Math + Science) divided by $2$ must be greater than $85$.

Determining the Median Science Score

The Science scores are: $78, 82, 87, 85, 79, 88, 81, 80$.

Sort the data from smallest to largest: $78, 79, 80, 81, 82, 85, 87, 88$.

Since there are $8$ data points, the median is the average of the 4th and 5th data points:

Students who satisfy the first condition (Science Score $> 81.5$) are:

• Boni ($82$)
• Cindy ($87$)
• Dita ($85$)
• Fani ($88$)

The other students (Ayu, Erfan, Gilang, Herman) have Science scores below the median, so they automatically do not pass.

Checking the Average Score Condition

Now we check the second condition for students who passed the first condition:

1. Boni:

   $$\text{Average} = \frac{92 + 82}{2} = \frac{174}{2} = 87$$

   Since $87 > 85$, Boni Passes.

2. Cindy:

   $$\text{Average} = \frac{90 + 87}{2} = \frac{177}{2} = 88.5$$

   Since $88.5 > 85$, Cindy Passes.

3. Dita:

   $$\text{Average} = \frac{86 + 85}{2} = \frac{171}{2} = 85.5$$

   Since $85.5 > 85$, Dita Passes.

4. Fani:

   $$\text{Average} = \frac{88 + 88}{2} = \frac{176}{2} = 88$$

   Since $88 > 85$, Fani Passes.

So, there are $4$ students who pass out of a total of $8$ students.

Calculating Quantity $P$

Comparing $P$ and $Q$

Given $Q = 65\%$.

Thus: