If X1 ¯ and X2¯ the means of two distributions such that X1

# If  the means of two distributions such that  is the mean of the combined distribution then

1. A

$\overline{X}<{\overline{X}}_{1}$

2. B

$\overline{X}>{\overline{X}}_{2}$

3. C

$\overline{X}=\frac{{\overline{X}}_{1}+{\overline{X}}_{2}}{2}$

4. D

${\overline{X}}_{1}<\overline{X}<{\overline{X}}_{2}$

Register to Get Free Mock Test and Study Material

+91

Verify OTP Code (required)

### Solution:

Let ${n}_{1}$ and ${n}_{2}$ be the number of observations in two groups having means ${X}_{1}$ and ${X}_{2}$ respectively. Then

$\overline{X}=\frac{{n}_{1}{\overline{X}}_{1}+{n}_{2}{\overline{X}}_{2}}{{n}_{1}+{n}_{2}}$

Now,

Register to Get Free Mock Test and Study Material

+91

Verify OTP Code (required)