Question

The mean age of a group of 100 children was 9.35 years .The mean age of 25 of them was 8.75 years and another 65 of them was 10 . 51 years. What is the mean age of the remaining children ?

Answer 1

Given:

✰ The mean age of a group of 100 children was 9.35 years.

✰ The mean age of 25 of them was 8.75 years.

✰ The mean age of 65 of them was 10.51 years.

To find:

✠ What is the mean age of the remaining children?

Solution:

Let's understand the concept first!

• First we will assume the mean age of the remaining children x.
• We know that the mean age of 25 of them was 8.75 years and another 65 of them was 10.51 years. So, we are provided with the mean age of total 90 children and we know that the there is a group of total 100 children, so the remaining children are 10.
• We will find the sum of ages of 100 children and then the sum of of ages of 25 and 65 children respectively,
• then we will add all the number of children which is equal to the sum of age of the total children.
• Thus, forming a requisite equation and doing the required calculations, we will find the value of x which is equal to the mean age of remaining children.

Lets find out...✧

➛ Mean age of 100 children = 9.35 years

➛ Sum of the ages of 100 children = 9.35 × 100

➛ Sum of the ages of 100 children = 935 years

Now,

➛ Mean age of 25 of them = 8.75 years

➛ Sum of the ages of 25 of them = 8.75 × 25

➛ Sum of the ages of 25 of them = 218.75 years

➛ Mean age of 65 of them = 10.51 years

➛ Mean age of 65 of them = 10.51 × 65

➛ Mean age of 65 of them = 683.15 years

Let the mean age of remaining 10 children be x.

➛ Mean age of 10 of them = x years

➛ Mean age of 10 of them = x × 10

➛ Mean age of 10 of them = 10x years

Then,

➤ Sum of the ages of 100 children = Sum of the ages of 25 + 65 + 10

➤ 935 = 218.75 + 683.15 + 10x

➤ 935 = 901.9 + 10x

➤ 10x = 935 - 901.9

➤ 10x = 33.1

➤ x = 33.1/10

➤ x = 3.31

∴ The mean age of the remaining children = 3.31 years

_______________________________

Answer 2

Mean age of remaining children = 3.31 years

Let xₙ denote the age of nᵗʰ child.

It is given that the mean age of 100 children is 9.35 years.

i.e., (x₁ + x₂ + ... + x₁₀₀ ) / 100 = 9.35

x₁ + x₂ + ... + x₁₀₀ = 100 × 9.35 = 935 ....(1)

Given that mean age of 25 of them is 8.75 years.

so , (x₁ + x₂ + ... + x₂₅) / 25 = 8.75

x₁ + x₂ + ... + x₂₅ = 8.75 × 25 = 218.75 ...(2)

Now, mean age of 65 children is 10.

(x₁ + x₂ + ... + x₆₅) / 65 = 10.51

x₁ + x₂ + ... + x₆₅ = 10.51 × 65 = 683.15 ...(3)

Now we have the sum of ages of 25 children and another 65 children. We have to find sum of ages of remaining 10 children. For that ,

Substituting (2) and (3) into (1).

218.75 + 683.15 + x₁ + x₂ + ... x₁₀ = 935

x₁ + x₂ + ... + x₁₀ = 935 - ( 218.75 + 683.15 )

= 935 - 901.9

= 33.1

Mean age of remaining 10 children = 33.1 / 10

= 3.31

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