Mean → Think Sum
Idea · Beginner
Problem Solving
A class of 20 students has an average score of 70. Another class of 30 students has an average score of 80. Find the average score of all 50 students.
First class total: 20 · 70 = 1400
Second class total: 30 · 80 = 2400
Total score: 3800
Total students: 50
Therefore,
Notice that the answer is not
because the groups have different sizes.
The average of n numbers is 20. After adding the number 50, the average becomes 22. Find n.
The original sum is 20n
After adding 50, there are n + 1 numbers with average 22, so
Thus
The average of n numbers is 30. When the largest number is removed, the average decreases to 28. When the smallest number is removed instead, the average increases to 31.
The difference between the largest and smallest numbers is 27. Find n.
Let the original sum be 30n
If the largest number L is removed,
so L = 2n + 28
If the smallest number S is removed,
so S = 31 - n
We know L - S = 27
Therefore,