TITLE: How to find mean and median from histogram
QUESTION [14 upvotes]: Solution for finding   mean : 

The problem  faced  when i saw a  video to evaluate the mean https://www.youtube.com/watch?v=vMrc6dP8pCo
According to the video, the lecturer said that, we can take the average of the measurement intervals. so according to him: 
we will get $$2.5 \times 15 +8.5\times 35+ ...$$
instead of $$1 \times 15 +6\times 35+ ...$$
Can we evaluate the mean and median precisely from the Histogram?

REPLY [2 votes]: You cannot compute the sample mean of all of the data without knowledge of all of the data.  The histogram, as given above, does not give all of the data.  The histogram is just a crude picture.   Any calculation from a histogram that allows more than one single value in each column will be at best an ESTIMATE of the sample mean.  
However, that might be OK for a lot of purposes...