The average of 37 numbers is 80. The average of the first 19 numbers is 75 and the average of the last 19 numbers is 84. If the 19
th
number is excluded, what is the average of the remaining numbers (approximate to one decimal place)?
- A82.5
- B80.5
- C77.5
- D87.5
Solution & Step-by-step Explanation
Let the total sum of 37 numbers be S
37
=37×80=2960.
Sum of the first 19 numbers =19×75=1425.
Sum of the last 19 numbers =19×84=1596.
Since the 19
th
number is common to both sets:
Sum of 19th number=(Sum of first 19)+(Sum of last 19)−S
37
19th number=1425+1596−2960=3021−2960=61
Excluding the 19
th
number, the new sum for 36 numbers is:
New Sum=2960−61=2899
New average of the remaining 36 numbers:
New Average=
36
2899
≈80.52≈80.5
37
=37×80=2960.
Sum of the first 19 numbers =19×75=1425.
Sum of the last 19 numbers =19×84=1596.
Since the 19
th
number is common to both sets:
Sum of 19th number=(Sum of first 19)+(Sum of last 19)−S
37
19th number=1425+1596−2960=3021−2960=61
Excluding the 19
th
number, the new sum for 36 numbers is:
New Sum=2960−61=2899
New average of the remaining 36 numbers:
New Average=
36
2899
≈80.52≈80.5