referring to this video, it was only briefly mentioned that “Usually, but not all the time, IQR is less than true range”. The “not all the time” just refers to the fact that IQR COULD be equal to True Range, but it can never be bigger, right?
Sure
Yes, the IQR can never be bigger than the range. However, it can be smaller than or equal to the range.
Take the list 1,2,3,4,5. The IQR = Q3 - Q1 = 4 - 2 = 2 while the range is larger (Range = 5 - 1 = 4).
Take the list 1,1,1,1,1. The IQR = Q3-Q1=1-1 = 0 while the range is equal (range = 1-1 = 0).
However, the IQR can never be larger than the range since the most spread out that Q1 and Q3 can be is when Q3 = max of the list and Q1 = min of the list. In that case, IQR = Q3 - Q1 = max - min = range.