How to Find Average After Removing a Member?
Average After Removing a Member questions require recalculating the total after subtracting one member’s value. If the original average and number of members are known, find the original total first, subtract the removed value, and divide by the remaining members. This page explains the formulas, common cases, shortcuts and solved examples.
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What Is the Average After Removing a Member?
If n members have an average of A and a member with value x is removed, the original total is nA. The remaining total is nA − x, and the number of members becomes n − 1. Therefore, the new average is (nA − x) ÷ (n − 1).
Average After Removing a Member Video Lessons
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Average: Adding or Removing a Member
Learn how adding or removing a member affects the average, and understand the calculation method for finding the new average in quantitative aptitude problems.
Average After Removing a Member Formula & Tricks
Important Formulas
Here, n is the original number of members, A is the original average, and x is the value of the removed member.
Multiply the original number of members by the original average.
This form shows that removing a value above the original average decreases the average, while removing a value below the average increases it.
If B is the new average after removal, the removed value can be found by subtracting the new remaining total from the original total.
Subtract the total of all removed values and divide by the number of members left.
Quick Tricks
If the removed value is greater than the original average, the new average decreases. If it is less than the original average, the new average increases. If it equals the original average, the average remains unchanged.
The decrease in average after removing x is (x − A) ÷ (n − 1), when x is greater than A. The increase is (A − x) ÷ (n − 1), when x is less than A.
Avoid averaging individual values again. First calculate the original total as nA, subtract the removed value, then divide by n − 1.
Average After Removing a Member Concepts
Finding the New Average When the Original Average Is Given
For n members with average A, if value x is removed, use B = (nA − x) ÷ (n − 1). The units of B are the same as the units of A and x.
Finding the Removed Member from Two Averages
If the original average is A for n members and the new average is B for n − 1 members, then removed value x = nA − (n − 1)B. This also indicates whether the removed value was above or below the original average.
Effect of Removing a Member on the Average
From B − A = (A − x) ÷ (n − 1), the sign of the change depends on A − x. If x = A, then B = A, so the average does not change.
Removing Multiple Members
If k members with total value R are removed from n members whose average is A, the new average is (nA − R) ÷ (n − k). The denominator is n − k, not n − 1.
Average After Removing a Member Data Table
Use the structured data below while following the explanation and examples.
Formula Selection for Removal Questions
Use the formula that matches the information given in the question.
| Given information | Required result | Formula |
|---|---|---|
| Original average A, members n, removed value x | New average | (nA − x) ÷ (n − 1) |
| Original average A, members n, new average B | Removed value | nA − (n − 1)B |
| Original average A, members n, removed total R, members removed k | New average | (nA − R) ÷ (n − k) |
| Original average A, members n, removed value x | Change in average | (A − x) ÷ (n − 1) |
Note: A positive change means the new average is higher; a negative change means it is lower.
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Average After Removing a Member: Revision Points
Use totals and the remaining number of members to recalculate the average accurately.
- Original total = number of members × original average.
- After removing one value x, remaining total = nA − x.
- Number of remaining members = n − 1.
- New average = (nA − x) ÷ (n − 1).
- Removed value = nA − (n − 1)B when the two averages are known.
- Removing a value above the original average lowers the average.
- Removing a value below the original average raises the average.
- For k removals, use (nA − sum of removed values) ÷ (n − k).
Average After Removing a Member FAQs
What is the average after removing one member formula?
If n members have average A and the removed member has value x, the new average is (nA − x) ÷ (n − 1).
The average of 6 students is 18. One student scoring 23 leaves. What is the new average?
Original total = 6 × 18 = 108. New average = (108 − 23) ÷ 5 = 85 ÷ 5 = 17.
How do you find the removed member when both averages are given?
Use x = nA − (n − 1)B, where A is the original average and B is the new average. For example, if n = 8, A = 20 and B = 19, x = 8 × 20 − 7 × 19 = 27.
What happens when the removed member has exactly the original average?
The average remains unchanged. For example, removing a value of 25 from a group whose average is 25 gives a new average of 25.
The average of 9 numbers is 14. A number is removed and the average becomes 13. What was the number?
Removed number = 9 × 14 − 8 × 13 = 126 − 104 = 22.
How is the formula changed when two members are removed?
Subtract the sum of both removed values from the original total and divide by n − 2. Thus, new average = (nA − x₁ − x₂) ÷ (n − 2).