relationship between mean ,median and mode

An empirical relationship exist between mean median and mode.for a moderately skewed distribution it is:

mean - mode=3(mean - median)


case 1: If a frequency distribution has a symmetrical frequency curve,the mean ,median and mode are equal 

case 2:If the frequency distribution is positively skewed,then the mean is greater than median and median is greater than mode

case 3:if the frequency distribution is negatively skewed,then mean is less than median and median is less than mode

since median always lies between mean and mode in a moderately skewed distribution,therefore it is considered as most realistic measure of central tendency

problem 1  for a moderately skewed distribution mode = 50.04 , mean =4.find median

solution

problem 2  if median =20 and mean = 22.5 in a moderately skewed distribution then compute the approximate value of the mode.

solution: