Question 11

Explanation

Given the mathematics scores of three student groups:

Group 1: $8, 2, 5, 8, 7$

Group 2: $6, 9, 7$

Group 3: $3, b, 10, 8$

The sum of the mode of Group 1's scores and the median of Group 2's scores is equal to $2$ times the average of Group 3's scores.

Step 1: Determine the mode of Group 1

Group 1 data: $8, 2, 5, 8, 7$

Frequency of each value:

• $2$ appears $1$ time
• $5$ appears $1$ time
• $7$ appears $1$ time
• $8$ appears $2$ times

The mode of Group 1 is $8$.

Step 2: Determine the median of Group 2

Group 2 data: $6, 9, 7$

Sort the data: $6, 7, 9$

Since the number of data points is odd ($3$), the median is the middle value, which is $7$.

Step 3: Determine the average of Group 3

Group 3 data: $3, b, 10, 8$

Average of Group 3:

Step 4: Set up the equation

Based on the given information:

Multiply both sides by $2$:

So the value $b = 9$, thus $P = 9$ and $Q = 8$.

Since $P = 9$ and $Q = 8$, we have $P > Q$.

Therefore, quantity $P$ is greater than quantity $Q$.