Average Calculation Steps
The problem requires finding the average of the last four numbers given the overall average and the average of the first six numbers.
1. Calculate the Total Sum of Ten Numbers
- The average of ten numbers is given as 50.
- The sum of a set of numbers is calculated as: Sum = Average × Count.
- Total sum of ten numbers = $50 \times 10 = 500$.
2. Calculate the Sum of the First Six Numbers
- The average of the first six numbers is given as 45.
- Sum of the first six numbers = $45 \times 6 = 270$.
3. Calculate the Sum of the Last Four Numbers
- The sum of the last four numbers can be found by subtracting the sum of the first six numbers from the total sum of the ten numbers.
- Sum of the last four numbers = (Total sum of ten numbers) - (Sum of the first six numbers)
- Sum of the last four numbers = $500 - 270 = 230$.
4. Calculate the Average of the Last Four Numbers
- The average of the last four numbers is calculated by dividing their sum by the count (which is 4).
- Average of the last four numbers = $\frac{\text{Sum of the last four numbers}}{\text{Count}}$
- Average of the last four numbers = $\frac{230}{4} = 57.5$.
Similar Questions
- The average of a group of 8 consecutive even numbers is 41. What is the sum of the smallest and largest numbers in the group?
- The average of x and y is 30. The average of x, y, and z is 40. What is the average of x, y, and 2z?
- The average weight of 10 boxes is 15.5 kg. If the heaviest box weighs 21 kg and the lightest weighs 10 kg, what is the average weight of the remaining boxes?
- The average of a group of 11 numbers is 61. If the first six numbers have an average of 57 and the last six numbers have an average of 65, what is the sixth number?
- The average of a certain number of quantities is 45. If 5 is added to each quantity, what will be the new average?
- A group of 5 friends went to a restaurant. If 4 of them paid Rs. 200 each and the fifth paid Rs. x, the average bill per person came out to be Rs. 210. What is the value of x?
- A trader bought 5 varieties of rice whose weights are in the ratio 2:3:4:5:6. Their respective prices per kg are Rs. 40, Rs. 42, Rs. 45, Rs. 48, and Rs. 50. What is the average cost per kg of the mixture?
- The average salary of 40 workers in a factory is Rs. 24,000. If the salary of a supervisor is added, the average rises to Rs. 24,500. What is the supervisor’s salary?
- The average temperature of a city from Monday to Friday is $40^{\circ}\text{ C}$. If the temperature on Saturday is $45^{\circ}\text{ C}$, what will be the average temperature from Monday to Saturday?
- The average age of 10 students in a class increases by 1 year when a 30-year-old teacher joins them. What was the original average age of the students?
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?
