The problem requires determining the new average when each number of a set is divided by 3, given that the original average is 15.
- The average of a set of numbers is calculated as the sum of the numbers divided by the total count of numbers.
Let us denote the sum of the original five numbers as \(S\). Given that the average is 15, we have: \(\frac{S}{5} = 15\). - From the equation in step 1, we can find \(S\):
\(S = 15 \times 5 = 75\)
- When each number is divided by 3, the sum of the new numbers becomes \(\frac{S}{3}\).
Thus, the sum of the numbers becomes:
\(\frac{75}{3} = 25\)
- Now, calculate the average of the new set of numbers. Since the total count remains the same (five numbers), the new average will be:
\(\frac{25}{5} = 5\)
Thus, the average of the new set of numbers when each number is divided by 3 becomes 5.
The correct answer is 5, which matches the provided correct answer.
Important Questions from Average
The average of 28 numbers is 77. The average of first 14 numbers is 74 and the average of last 15 numbers is 84. If the 14 th number is excluded, then what is the average of remaining numbers? (correct to one decimal places)
24 students collected money for donation. The average contribution was Rs. 50. Later on, their teacher also contributed some money. Now the average contribution is Rs. 56. The teacher’s contribution is:
Out of 6 numbers, the sum of the first 5 numbers is 7 times the 6 th number. If their average is 136, then the 6 th number is:
The average of five numbers is 30. If one number is excluded, then average becomes 31. What is the excluded number?
The average weight of 49 students in a class is 39 kg. Seven of them whose average weight is 40 kg leave the class and other seven students whose average weight is 54 kg join the class. What is the new average weight (in kg) of the class?
