Question

In the class of 25 students, the average score is 84. Six students in the class each received a maximum score of 100, and three students each received a score of 60. What is the average score of the remaining students?

Short answer

The score of the remaining students is 82.5.

Step-by-step solution

Step 1. Find the remaining number of people.

There are 6+3 people whose scores are known and 25 total people.

So, the number of remaining people is

$25-\left(6+3\right)=16$

Step 2. Find the sum of all scores.

First, find the average, divide the sum by the number of items.

Hence, the sum is the average multiplied by the number of items.

There are 25 people and the average score is 84. Multiply these to find the sum of all the scores:

$84\times 25=2100$ …(1)

Step 3. Find the sum of the unknown scores of the remaining 16 people.

First, multiply each known score by the number of people that earned that score and add the totals.

6 people each scored 100

3 people each scored 60

So, we have

$6\left(100\right)+3\left(60\right)=600+180$

$=780$ … (2)

Subtract (2) from (1), we get

$2100-780=1320$

Step 4. Find the average of the remaining 16 people.

To find this, divide 1320 by 16:

$\frac{1320}{16}=82.5$

Hence, the score of the remaining students is 82.5.