Question

The average age of a group of 8 persons was 14 years. A person with age 28 years left the group and a new person with age 16 years joined the group. Find the new average age of the group. *
13 ਸਾਲ(years)
14 ਸਾਲ(years)
15.5 ਸਾਲ(years)
12.5 ਸਾਲ(years)

Answer 1

X1+x2+X3+x4+x5+x6+x7+x8/8=14

X1+x2+X3+x4+x5+x6+x7+x8=112

28+x2+X3+x4+x5+x6+x7+ x8=112

x2+X3+x4+x5+x6+x7+x8=112-28=84

and new person joined with 16 years

X1=16

X1+x2+X3+x4+x5+x6+x7+x8=

16+x2+X3+x4+x5+x6+x7+x8=

16+84=100

average = 100/8=12.5 years

Answer 2

Given:

The average age of a group of 8 persons was 14 years. A person with age 28 years left the group and a new person with age 16 years joined the group.

To find:

The new average age of the group.

Solution:

The new average age of the group is 12.5

To answer this question, we will follow the following steps:

As we know,

$average \: = \frac{sum \: of \: observations}{number \: of \: observations}$

Now,

As given, we have,

The average age of a group of 8 persons = 14 years.

So,

The sum of ages of 8 persons

$= 14 \times 8$

$= 112 \: years$

Now,

A person with age 28 years left the group and a new person with age 16 years joined the group.

So,

The total number of persons remain the same i.e. 8

The sum of age of 8 persons

$= 112 - 28 + 16$

$= 100 \: years$

The new average age of 8 persons

$= \frac{100}{8}$

$= 12.5$

Hence, the new average of the group is 12.5