Question

The mean weight of 150 students is 60 kg. The mean weight of boys is 70 kg with a standard deviation 10 kg. For the girls, the mean weight is 55 kg and the standard deviation is 15 kg. Find the Number of boys and girls.

Answer 1

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Answer 2

Answer:

Let the number of boys and girls in the class be n₁ and n₂ respectively. Then

n₁ + n₂ = 150 — (i)

We have

x₁ = Mean weight of boy = 70 kgs

x₂ = Mean weight of girls = 55 kgs

x = Mean weight of all students = 60 kgs

∴ x = (n₁ x₁ + xn₂) / (n₁ + n₂)

⇒ 60 = (n₁ × 70 + n₂ × 55)/ (n₁ + n₂)

⇒ 60 (n₁ + n₂) = 70n₁ + 55n₂

⇒ 60n₁ + 60n₂ = 70n₁ + 55n₂

⇒ 10n₁ = 5n₂

⇒ 2n₁ = n₂ — (ii)

• Putting n₂ = 2n₁ from (ii) in (i), we get

⇒ n₁ + 2n₁ = 150

⇒ 3n₁ =150

⇒ n₁ = 50

• Putting n₁ = 50 in n₂ = 2n₁ we get

⇒ n₂ = 100

∴ 50 boys & 100 girls in the class.