Practice Questions
Concept Explanation
When a value is removed from a set, the new average is:
New average = (Old sum − Removed value) / (n − 1)
Key Idea
- Old sum = Old average × n
- New sum = Old sum − removed value
- Change in average = (Old average − Removed value) / (n − 1)
Placement Shortcut
Find total sum first, subtract the removed value, then divide by one less count.
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Q1 EasyThe average of 6 numbers is 30. If one number is excluded, the average of the remaining numbers becomes 28. The excluded number is:ExplanationOld sum = 6 × 30 = 180. New sum of 5 numbers = 5 × 28 = 140. Excluded number = 180 − 140 = 40. Hence the answer is 40.
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Q2 EasyThe average of 9 numbers is 18. If one number is excluded, their average becomes 16. The excluded number is:ExplanationOld sum = 9 × 18 = 162. New sum of 8 numbers = 8 × 16 = 128. Excluded number = 162 − 128 = 34. Hence the answer is 34.
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Q3 EasyThe average of five numbers is 29. If one number is excluded, the average becomes 27. The excluded number is:ExplanationOld sum = 5 × 29 = 145. New sum of 4 numbers = 4 × 27 = 108. Excluded number = 145 − 108 = 37. Hence the answer is 37.
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Q4 EasyThe average of 6 numbers is 25. If 40 is removed, the new average is:ExplanationOld sum = 6 × 25 = 150. Remaining sum = 150 − 40 = 110. New average = 110 / 5 = 22. Hence the answer is 22.
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Q5 EasyThe average of 8 numbers is 22. If a number equal to the average is removed, the new average is:ExplanationOld sum = 8 × 22 = 176. Removing 22 leaves sum = 154 and count = 7. New average = 154 / 7 = 22. Removing a value equal to the average leaves the average unchanged. Hence the answer is 22.
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Q6 EasyFive students have an average weight of 72 kg. One student weighing 60 kg leaves. The new average is:ExplanationOld sum = 5 × 72 = 360 kg. Remaining sum = 360 − 60 = 300 kg. New average = 300 / 4 = 75 kg. Hence the answer is 75 kg.
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Q7 MediumThe average of 50 numbers is 30. If two numbers 65 and 35 are discarded, the average of the remaining numbers is:ExplanationOld sum = 50 × 30 = 1500. Sum discarded = 65 + 35 = 100. Remaining sum = 1500 − 100 = 1400. Remaining count = 48. New average = 1400 / 48 = 175 / 6 = 29 1/6. Hence the answer is 29 1/6.
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Q8 MediumThe average weight of 45 students is 52 kg. If 5 students of average weight 48 kg leave the group, the new average weight is:ExplanationOld sum = 45 × 52 = 2340 kg. Sum of the 5 students who leave = 5 × 48 = 240 kg. Remaining sum = 2340 − 240 = 2100 kg. Remaining students = 40. New average = 2100 / 40 = 52.5 kg. Hence the answer is 52.5 kg.
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Q9 MediumThe average of 10 numbers is 40. If 55 is removed, the new average is:ExplanationOld sum = 10 × 40 = 400. Remaining sum = 400 − 55 = 345. New average = 345 / 9 = 115 / 3 = 38 1/3. Hence the answer is 38 1/3.
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Q10 MediumThe average of 7 numbers is 18. If 32 is removed, the new average is:ExplanationOld sum = 7 × 18 = 126. Remaining sum = 126 − 32 = 94. New average = 94 / 6 = 47 / 3 = 15 2/3. Hence the answer is 15 2/3.
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Q11 HardThe average of 40 numbers is 36. When three numbers, namely 52, 48 and 36, are discarded, the average of the remaining numbers is:ExplanationOld sum = 40 × 36 = 1440. Sum discarded = 52 + 48 + 36 = 136. Remaining sum = 1440 − 136 = 1304. Remaining count = 37. New average = 1304 / 37 = 35 9/37. Hence the answer is 35 9/37.
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Q12 HardThe average of 5 numbers is 32. After removing one number, the average becomes 30. The removed number is:ExplanationOld sum = 5 × 32 = 160. New sum of 4 numbers = 4 × 30 = 120. Removed number = 160 − 120 = 40. Hence the answer is 40.
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Q13 HardA batsman's average after 10 innings is 45. If the highest score 95 is excluded, the new average is:ExplanationOld sum = 10 × 45 = 450. Remaining sum = 450 − 95 = 355. New average = 355 / 9 = 39 4/9. Hence the answer is 39 4/9.
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Q14 HardThe average of 15 numbers is 28. If 58 is removed, the new average is:ExplanationOld sum = 15 × 28 = 420. Remaining sum = 420 − 58 = 362. New average = 362 / 14 = 181 / 7 = 25 6/7. Hence the answer is 25 6/7.
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DS1 Easy
In a campus drill on data cleaning, one observation is dropped from a set. What is the new average after removing one number?
Statement IThe average of 6 numbers is 24.
Statement IIThe number removed is 30.
ExplanationNew average = (Old sum − removed value) / (n − 1). Statement I: Old sum = 144, but the removed value is unknown. Statement II: Removed value = 30, but old sum is unknown. Together: New average = (144 − 30) / 5 = 114 / 5 = 22.8. Both are needed. Answer: C. -
DS2 Easy
During an aptitude mock, candidates must decide whether dropping a value lowers the mean. Is the new average less than the old average?
Statement IThe removed number is 50.
Statement IIThe old average is 45.
ExplanationRemoving a value lowers the average if and only if it exceeds the old average. Statement I alone does not give the old average. Statement II alone does not give the removed value. Together: 50 > 45, so the new average is less. Both are needed. Answer: C.
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DS3 Medium
Which value was deleted from a list. What is the removed number?
Statement IThe average of 8 numbers is 20.
Statement IIAfter removal, the average of 7 numbers is 18.
ExplanationRemoved number = Old sum − New sum. Statement I: Old sum = 160. Statement II: New sum = 126. Alone, neither gives both. Together: Removed number = 160 − 126 = 34. Both are needed. Answer: C. -
DS4 Medium
A company screening item asks for the average after one observation is deleted. What is the new average?
Statement IThere are 5 numbers with average 16.
Statement IIThe number removed equals the average.
ExplanationStatement I: Old sum = 80, but without knowing what is removed the new average is unknown. Statement II: Says the removed number equals the average, but without n and the average value the result is unknown. Together: Removing 16 from a set of average 16 leaves average 16. Both are needed. Answer: C.