Question

Is the median always between Mean and Mode?

Answer 1

Checking if the median is always between mean and mode

The empirical formula relating the mean, median, and mode is given as:

$\mathrm{mean}-\text{mode}=3\left(\text{mean - median}\right)$

This means that the disparity between mean and mode is almost three times the difference between the mean and median.

In perfectly symmetrical data, the mean, mode and median will be the same.

If the data is less skewed then, $\text{mode > median > mean}$.

While, if the data is right-skewed, $\text{mean > median > mode}$

Hence, the median always between Mean and Mode.