Question

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? f. 81.0 g. 92.0 h. 94.0 j. 94.4 k. 96.6

Explanation:

Step1: Find the sum of the original four - number list

The formula for the average $\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}$. Given $n = 4$ and $\bar{x}=92.0$, then $\sum_{i=1}^{4}x_{i}=n\times\bar{x}=4\times92.0 = 368$.

Step2: Find the sum of the first three numbers

Let the four numbers in the original list be $a,b,c,d$. So $a + b + c+d=368$. We know $d = 40$, then $a + b + c=368 - 40=328$.

Step3: Find the average of the new list

The new list has numbers $a,b,c,48$. The sum of the new list is $a + b + c+48$. Since $a + b + c = 328$, the sum of the new list is $328+48=376$. The number of elements in the new list $n = 4$. The average of the new list $\bar{y}=\frac{376}{4}=94.0$.

Answer:

G. 92.0