Shortcut Methods For Average - 3

New Average when a person joines the group.

Rule 1:

In case of increase in average

Age of new member = Previous average + ( Increase in average × Number of members including new member)

Example

The average age of 15 boys is 17 years and is increased by 0.5 years when a new boy is joined in the group. What is the average of new boy?

Sol:

Age of new member = Previous average + ( Increase in average × Number of members including new member)

Previous average = 17 years

Increase in average = 0.5 years

Number of members including new member = 16

So,

Age of new member = 17 + ( 0.5 × 16) = 17 + 8 = 25 years.

Rule 2:

In case of decrease in average

Age of new member = Previous average - ( Decrease in average × Number of members including new member)

Example

The average age of 10 girls is 23 years and is decreased by 0.5 years when a new girl is joined in the group. What is the age of new girl?

Sol:

Age of new member = Previous average - ( Decrease in average × Number of members including new member)

Previous average = 23 years

Decrease in average = 0.5 years

Number of members including new member = 11

Age of new member = 23 – ( 0.5 × 11) = 23 – 5.5 = 17.5 years

Rule 3:

New average of group =
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Example

A group of 20 members having average age of 25 years has a new member aged 25 years. What is new average of the group?

Sol:

New average of group =

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Previous average = 25 years

Number of persons excluding new member = 20

Age of new member = 25 years

Number of persons including new member = 21

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