The average of a list of 4 numbers is 92.0. A new list of 4 numbers has the same first 3 numbers as the original list, but the fourth number in the original list is 40, and the fourth number in the new list is 48. What is the average of this new list of numbers?

Summary Submit Skip Question

Since there are only four numbers in both list, increasing the sum of the numbers by 8 increases the average by \(\dfrac{8}{2} =4\).

Here is the first list:

$$ L_1 = \{x_1, x_2, x_3, 40\} $$

The average or mean is:

$$ 90 = \frac{x_1+x_2+x_3+40}{4} $$ $$ 360 = x_1+x_2+x_3+40 $$ $$ x_1+x_2+x_3 = 320 $$

The second list has the same first three numbers:

$$ L_2 = \{x_1, x_2, x_3, 48\} $$

The average is:

$$ \overline{x} = \frac{x_1+x_2+x_3+48}{4} $$ $$ \overline{x} = \frac{320+48}{4} $$ $$ = \frac{368}{4} = \boxed{94} $$