How to Calculate New Average After Adding a Member?

Average After Adding a Member problems compare the original total with the total after one new value is included. If a group has n members and average a, its total is na. After adding a member with value x, the new average is found by dividing na + x by n + 1.

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What Is the Average After Adding a Member?

When one member is added to a group, the new average equals the new total divided by the new number of members. If the original average is a and the original number of members is n, the new total is na + x when the added member has value x.

The average after adding a member is calculated as (na + x)/(n + 1). If the new average b is known, the added member's value is x = (n + 1)b - na. The new average increases when x is greater than the old average and decreases when x is less than the old average.

Average After Adding 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.

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Average After Adding a Member Formula & Tricks

Important Formulas

New average after adding one member
New average = (na + x)/(n + 1)

Here, n is the original number of members, a is the original average, and x is the value of the added member.

Value of the added member
x = (n + 1)b - na

Here, b is the new average after adding the member.

Added member from change in average
x = a + (n + 1)d

If the average changes by d, where d = new average - old average, the added member's value is a + (n + 1)d.

Change in average
d = (x - a)/(n + 1)

The increase or decrease in average equals the difference between the added value and old average divided by the new number of members.

Quick Tricks

Use total instead of averaging repeatedly

First find the original total as number of members multiplied by the old average. Add the new member's value, then divide by the new count.

Example: For 8 members with average 24, the total is 8 × 24 = 192. After adding 32, the new average is (192 + 32)/9 = 224/9.
Compare the added value with the old average

If the added value is above the old average, the average rises; if it is below the old average, the average falls. The change is (x − a)/(n + 1).

Example: If a = 40, n = 9 and x = 50, the average rises by (50 − 40)/10 = 1.

Average After Adding a Member Concepts

Finding the New Average When the Added Value Is Known

Multiply the old average by the original number of members, add the new member's value, and divide by the new number of members.

For n members with average a, the old total is na. After adding value x, the total becomes na + x and the count becomes n + 1. Therefore, the new average is (na + x)/(n + 1).

Example: The average marks of 6 students is 18. A seventh student scores 25. New average = (6 × 18 + 25)/7 = 133/7 = 19.

Finding the Added Member When the New Average Is Known

The added member's value is obtained by subtracting the old total from the new total.

If the old average is a for n members and the new average is b for n + 1 members, then old total = na and new total = (n + 1)b. Hence, added value = (n + 1)b − na.

Example: The average age of 10 people is 24 years. After one person joins, the average becomes 25 years. The new person's age = 11 × 25 − 10 × 24 = 275 − 240 = 35 years.

Effect of the Added Member on the Average

The change in average depends on how far the added value is from the old average.

The change is d = (x − a)/(n + 1). A value equal to the old average causes no change. A value greater than the old average increases the average, while a smaller value decreases it.

Example: For 5 members with average 30, adding a member with value 24 changes the average by (24 − 30)/6 = −1. The new average is 29.

Finding the Original Average or Group Size

The same total-based equations can be rearranged to find a missing original average or number of members.

If the added value x, old average a and new average b are known, the original count satisfies na + x = (n + 1)b, so n(a − b) = b − x and n = (b − x)/(a − b), when a is not equal to b.

Example: A new member with value 20 lowers an average from 26 to 25. The original count is (25 − 20)/(26 − 25) = 5.

Practice Average After Adding a Member Questions

Practise published questions related to this topic.

1The price of petrol is increased by 28%. A person wants to increase his expenditure by 22% only. By approximately what percent should he decrease his consumption?→ 2An article is sold for Rs. 288 after successive discounts of 20% and 25%. What is the marked price of the article?→ 321.6 ÷ 3.6 × 2 + 0.25 × 16 ÷ 4 - 6 is equal to∶→ 4What is the value of x so that the seven digit number 55350x2 is divisible by 72?→ 5Two articles are sold for Rs. 4,752 each. On one, the seller gains 32% and on the other he loses 28%. What is his overall gain or loss percentage, correct to one decimal place?→ 6The price of sugar is increased by 17%. A person wants to increase his expenditure by 5% only. By approximately what percent should he decrease his consumption?→ 7The value of 15.2 + 5.8 ÷ 2.9 × 2 - 3.5 × 2 ÷ 0.5 is equal to:→ 8What is the value of x so that the seven digit number 8439x53 is divisible by 99?→ 9Two articles are sold for Rs. 962 each. On one, the seller gains 30% and on the other he loses 26%. What is his overall gain or loss percentage, nearest to one decimal place?→ 10An article is sold for Rs. 288 after successive discounts of 25% and x%. If the marked price of the article is Rs. 480, what is the value of x?→

Average After Adding a Member Quick Quiz

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Quick Revision Notes

Average After Adding a Member: Revision Points

Use totals and the new count to solve every one-member addition problem.

  • Original total = original number × original average.
  • New total after addition = old total + value of added member.
  • New average = (na + x)/(n + 1).
  • Added value = (n + 1)b − na.
  • Change in average = (x − a)/(n + 1).
  • The average remains unchanged only when the added value equals the old average.

Related Topic Explainers

Average → Simple Average → Combined Average → Average Based on Misread Numbers → Weighted Average → Average of Consecutive Numbers → Average of Arithmetic Progression →

Average After Adding a Member FAQs

What is the average after adding one member?

If n members have average a and the added member has value x, the new average is (na + x)/(n + 1).

How do you find the added member's value when the average changes?

Use x = a + (n + 1)d, where d is the change in average. For example, if a = 20, n = 7 and the average rises by 2, x = 20 + 8 × 2 = 36.

A group of 12 has average 15. If a member with value 28 joins, what is the new average?

Old total = 12 × 15 = 180. New average = (180 + 28)/13 = 208/13 = 16.

The average of 8 numbers is 21 and becomes 22 after one number is added. What is the added number?

Added number = 9 × 22 − 8 × 21 = 198 − 168 = 30.

When does adding a member leave the average unchanged?

The average remains unchanged when the added member's value equals the old average. For example, adding 18 to a group whose average is 18 does not change the average.

How is the original group size found if the added value and both averages are known?

Use n = (b − x)/(a − b), where a is the old average, b is the new average and x is the added value. If a = 26, b = 25 and x = 20, n = (25 − 20)/(26 − 25) = 5.

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