Weighted Median and Weighted Mode - Does it make any sense?

Weighted Median and Weighted Mode - Does it make any sense?

Mean, Median and mode are called the the measures of central tendency. 

Weighted mean make real sense as in your observations the data points are equipped with weights for each observation. Thus each data point is not equally responsible in mean calculation. We calculate it as 

 

Now in other words we can say that observation xi is repeated wi number of times so we have calculated the mean by the formula above.

When it comes to median, we first arrange the data points in ascending order and take the middle observation as the median. if the observations are in odd numbers we take the middle most value of the observations are even we take mean of two central observations. 

Weighted median is again calculated using the similar method, place each observation xi in wi number of times in ascending order. Now pickup the middle observation and call it weighted median. if the observations are in odd numbers we take the middle most value of the observations are even we take mean of two central observations. 

Mode is also a measure of central tendency, it is the most frequent observed data point which in the set of observation set. There can be multiple modes in a set of observation, such data is called multimodal data. It is obvious in case of weighted mode, the unique observation point which have highest total of weights associated will be the weighted mode.

So what do u say? does it make sense?