Question

the average age of 10 member of a dance group is 12 . Three members of age 9 ,10,11 years leave the group . A year later three new member of age 11,12,13 year respectively join the group . What is the average age of group now ?​

Answer 1

Answer:

13.3

Step-by-step explanation:

$Mean = \frac{\text{Sum of all ages}}{\text{Number of members}}$

$12 = \frac{\text{Sum of all ages}}{10}$

$12 \times 10 =\text{Sum of all ages}$

So, $120 =\text{Sum of all ages}$

So, sum of ages of 10 members is 120

Now Three members of age 9 ,10,11 years leave the group

Number of members = 10 -3 = 7

So, sum of ages = 120 -(9+10+11)= 90

So, the sum of ages of 7 members = 90

After a year each of the seven members age will be increased by 1 year

So,  After a year the sum of ages of 7 members = 90 + 7(1) =97

A year later three new member of age 11,12,13 year

So, New sum =  97+11+12+13 =133

So, $\text{New Average} = \frac{133}{10}=13.3$

So, the average age of group is 13.3 now .

Answer 2

Answer:

The average age of the group  now = 13.3

Step-by-step explanation:

Given,

The average age of 10 members of a dance group is 12

Three members of age 9,10,11 leave the group

A year later three new members of age 11,12,13 joined the group

To find,

The new average age group now

Solution:

Recall the concept:

Average = $\frac{Sum \ of \ observations}{Total \ number \ of \ observations}$

Since the average age of 10 members is 12, we have

12 = $\frac{Total\ age\ of \ 10\ people}{10}$

Total age of 10 people  = 12×10 = 120

Since three members of age 9 ,10,11 years leave the group, the total age of 7 people = 120 - (9+10+11) = 120 - 30 = 90

After one year the total age of 7 people = 97

Since a year later three new members of age 11,12,13 year respectively join the group, then the total age of 10 people = 97+ (11+12+13) = 97+36 = 133

New average age of the group = $\frac{133}{10}$ = 13.3

∴ The average age of the group  now = 13.3

SPJ2