Relation between median and arithmetic mean

descriptive statisticsmedian

The median of the numbers in a list is $x$, and the arithmetic mean of the numbers in the list is $\frac{x+1}2$.

Quantity $A = x$ and Quantity $B= \frac{x+1}2$

  1. Quantity $A$ is greater.
  2. Quantity $B$ is greater.
  3. The two quantities are equal.
  4. The relationship cannot be determined from the information given.

I think the answer is option $4$ ; because there is no information on how the data is distributed and whether the data is skewed to the right or skewed to the left.
But I am not sure about this answer.‌‌

Best Answer

In general, the median can be smaller than, equal to, or bigger than the mean.

Option 4 is the required answer, with the aforementioned possibilities corresponding to $x<1,\;x=1$ and $x>1,$ respectively.

Related Question