If $\bar{x}$ and $\bar{y}$ are the means of two distributions such that $\bar{x} \lt \bar{y}$ and $\bar{z}$ is the mean of the combined distribution, then which one of the following statements is correct?

• A

  $\bar{x} \lt \bar{y} \lt \bar{z}$
• B

  $\bar{x} \gt \bar{y} \gt \bar{z}$
• C

  $\bar{z}=\frac{\bar{x}+\bar{y}}{2}$
• Correct answer
  D

  $\bar{x} \lt \bar{z} \lt \bar{y}$

Hence, the correct answer is option: 'D'.