SSC CGL (Prelims) General: Statistics questions with solutions

Q1. A cricketer's average score over a series of matches is 42. If she scores 138 runs in the next match, her average increases to 46. How many matches had she played before this?

1. 23
2. 22
3. 24
4. 26

Answer: 23

If the average before the next match is 42 over \(n\) matches, total runs are \(42n\). After scoring 138, the average becomes 46 over \(n+1\) matches, so \(42n+138=46(n+1)\). Solving gives \(n=23\).

Q2. The average of 15 numbers is 72. The average of the first 6 numbers is 65. The average of the next 5 numbers is 20% higher than the average of the first 6. The 12th number is 8 less than the 15th, the 13th is 5 greater than the 15th, and the 14th number is 78. What is the average of the 12th and 13th numbers?

1. 73.5
2. 80
3. 78
4. 76.5

Answer: 73.5

Total sum of 15 numbers is \(15\times72=1080\). Sum of first 6 numbers is \(6\times65=390\), and sum of next 5 numbers is \(5\times78=390\). So the first 11 numbers sum to 780, leaving 300 for the last four numbers. Using the relations, the 15th number is 75, so the 12th and 13th are 67 and 80, whose average is 73.5.

Q3. The average weight of 11 players is 72 kg. If the coach's weight is excluded, the average decreases by 1 kg. What is the weight of the coach?

1. 81 kg
2. 82 kg
3. 83 kg
4. 84 kg

Answer: 82 kg

Total weight of 11 players and coach is not directly given, but the 11 players' average is 72 kg, so their total is \(11 \times 72 = 792\) kg. Excluding the coach leaves 10 players with average 71 kg, so their total is \(10 \times 71 = 710\) kg. Therefore, the coach's weight is \(792 - 710 = 82\) kg.

Q4. The average of a group of 9 numbers is 45. If the first five numbers have an average of 42 and the last five numbers have an average of 49, what is the fifth number?

1. 48
2. 50
3. 52
4. 54

Answer: 50

Total of 9 numbers = \(9\times45=405\). Sum of first five = \(5\times42=210\), and sum of last five = \(5\times49=245\). Their sum counts the fifth number twice, so fifth number = \(210+245-405=50\).

Q5. The average weight of 12 boxes is 20 kg. If the heaviest box weighs 25 kg and the lightest weighs 11 kg, what is the average weight of the remaining boxes?

1. 19.8 kg
2. 20.4 kg
3. 20.6 kg
4. 21.2 kg

Answer: 20.4 kg

Total weight of 12 boxes is $12\times 20=240$ kg. Removing the heaviest and lightest boxes leaves $240-(25+11)=204$ kg for 10 boxes, so the average is $204/10=20.4$ kg.

Q6. The average score of 40 students in an exam is 75. If the marks of one student were wrongly entered as 95 instead of 55, what is the correct average?

1. 74.5
2. 76
3. 74
4. 73.5

Answer: 74

The wrong total = 40 × 75 = 3000. Since 95 was entered instead of 55, the total is 40 marks too high, so correct total = 2960. The correct average = 2960/40 = 74.

Q7. The average of 5 different numbers is 24. If the smallest number is 15, what is the average of the remaining four numbers?

1. 27.25
2. 26.25
3. 25.5
4. 24.5

Answer: 26.25

The sum of 5 numbers is \(5\times24=120\). Removing the smallest number 15 leaves \(120-15=105\). The average of the remaining four numbers is \(105/4=26.25\).

Q8. The average of 12 results is 75. If the top two results are excluded, the average becomes 72. What is the average of the top two results?

1. 90
2. 84
3. 96
4. 99

Answer: 90

The total of 12 results is 12×75 = 900. After excluding the top two, the total of the remaining 10 results is 10×72 = 720. So the top two results sum to 180, and their average is 90.

Q9. The average score of a batsman in 20 innings is 42. If his highest score of 120 is excluded, what is the new average?

1. 37.89
2. 38.89
3. 39.89
4. 36.89

Answer: 37.89

The total score in 20 innings is \(20\times 42 = 840\). Excluding the highest score of 120 leaves \(840-120=720\), and the new average is \(720/19 \approx 37.89\).

Q10. In a group of 60 workers, the average monthly income per worker is ₹28,000. If 20 junior workers average ₹18,000 each, what is the average monthly income of the senior workers?

1. ₹33,000
2. ₹34,500
3. ₹35,000
4. ₹36,500

Answer: ₹33,000

Total income of 60 workers = \(60 \times 28000 = 16,80,000\). Income of 20 junior workers = \(20 \times 18000 = 3,60,000\). So income of 40 senior workers = \(16,80,000 - 3,60,000 = 13,20,000\), and their average = \(13,20,000/40 = 33,000\).