Calculating Batsman's New Average Score
The problem asks for the new average score of a batsman after excluding his highest score.
Initial Average Score Calculation
The batsman's average score across 20 innings is 42.
- Number of innings = 20
- Average score = 42
The total score of the batsman is calculated as:
Total Score = Average Score $\times$ Number of innings
Total Score = $42 \times 20 = 840$ runs
Adjusting for Highest Score Exclusion
The highest score of 120 runs is removed.
- Highest score = 120 runs
- New total score = Total Score - Highest score
- New total score = $840 - 120 = 720$ runs
When the highest score is excluded, the number of innings considered also decreases by one.
- New number of innings = 20 - 1 = 19
Calculating the New Average Score
The new average is calculated using the adjusted total score and the new number of innings.
New Average Score = $\frac{\text{New total score}}{\text{New number of innings}}$
New Average Score = $\frac{720}{19}$
New Average Score $\approx 37.8947$
Rounding to two decimal places, the new average score is 37.89.
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?
