Relationship between mean, median and mode

An empirical relationship exists between mean, median and mode. For a moderately skewed distribution it is:

• If a frequency distribution has a symmetrical frequency curve, the mean, median and mode are equal.

• If a frequency distribution is positively skewed, then mean is greater than median and median is greater than mode.

• If a 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: For a moderately skewed distribution mode = 50.04, mean = 45, Find median.