Assertion (A): The mean of x₁, x₂ and x₃ is m. Then the value of (x₁ - m) + (x₂ - m) + (x₃ - m) = 0.

Reason (R): x₁ + x₂ + x₃ = 3m

⇒ (x₁ - m) + (x₂ - m) + (x₃ - m) = (x₁ + x₂ + x₃) - 3m

1. A is true, but R is false.

2. A is false, but R is true.

3. Both A and R are true, and R is the correct reason for A.

4. Both A and R are true, and R is the incorrect reason for A.

Assertion (A): Mean of n observations is x and mean of another set of n observations is y, the combined mean of all the observations is $\dfrac{x + y}{2}$

Reason (R): Total number of observations = nx + ny

∴ Mean of all the observations = $\dfrac{nx + ny}{2n}$

1. A is true, but R is false.

2. A is false, but R is true.

3. Both A and R are true, and R is the correct reason for A.

4. Both A and R are true, and R is the incorrect reason for A.

The mean of 200 items was 50. Later on, it was discovered that two items were misread as 92 and 8 instead of 192 and 88. Find the correct mean.

Find the mean of 75 numbers, if the mean of 45 of them is 18 and the mean of the remaining ones is 13.