Question

The mean wage of 100 workers is 284. The mean wage of 70 workers is 290. Find the mean wage of remaining workers. 4

Answer 1

Answer:-

Given:

Mean wage of 100 workers = ₹ 284

Mean wage of 70 workers = ₹ 290

We know that,

Mean = Sum of observations/Number of observations

So,

⟹ Sum of wages of 100 workers/100 = ₹ 284

⟹ Sum of wages of 100 workers = ₹ 28400

Similarly,

⟹ Sum of wages 70 workers/70 = ₹ 290

⟹ Sum of wages of 70 workers = ₹ 20300

now,

Remaining workers = 100 - 70 = 30.

⟹ Sum of wages of 30 workers = ₹ 28400 - 20300

⟹ Sum of wages of 30 workers = ₹ 8100

So,

Mean wage = 8100/30 = ₹ 270

∴ The mean wage of remaining workers is ₹ 270.

Answer 2

Answer:

⊡ Mean Wages of 100 Workers (M₁) = 284

⊡ Mean Wages of 70 Workers (M₂) = 290

⊡ Mean Wages of 30 Workers (M₃) = ?

We can see that Mean Wages of 70 Workers is more than that of 100 Workers.

Hence, Wages of those 70 Workers is More in compare to 30 Workers.

Extra Mean Wages of those 70 Workers will be Adjust from those 30 Workers.

• According to the Question :

⇒ 70 × Extra Mean = 30 × Extra Mean

⇒ 70 × (M₂ - M₁) = 30 × (M₁ - M₃)

⇒ 70 × (290 - 284) = 30 × (284 - M₃)

⇒ 70 × 6 = 30 × (284 - M₃)

⇒ 420 ÷ 30 = (284 - M₃)

⇒ 14 = 284 - M₃

⇒ M₃ = 284 - 14

⇒ M₃ = 270

∴ Hence, Mean of remaining worker is 270.