Question

a group of 5 students received their test scores. the average of the 4 lowest scores is 81 and the average of the 4 highest scores is 93 .what is the difference between the maximum and minimum possible average scores overall?​

Answer 1

Given: A group of 5 students received their test scores. the average of the 4 lowest scores is 81 and the average of the 4 highest scores is 93.

To find: We have to find the difference between the maximum and minimum possible average scores overall.

Solution:

Let the highest score be x and the lowest score is y.

Now let the sum of the middle three scores be z.

The average of the 4 highest scores is 93

So, we can write-

$\frac{x + z}{4} = 93 \\ x +z = 372 \\ x = 372 - z$

Again, the average of the 4 lowest scores is 81.

So, we can write

$\frac{y + z}{4} = 81 \\ y + z = 324 \\ y = 324 - z$

Now the difference between the maximum and minimum marks is

$x - y = 372 - z - 324 + z \\ x - y = 48$

So, the difference between the maximum and minimum possible average scores overall is 48.