When we say a statistic is resistant, we mean the extreme values do not affect the statistic to a large extent or to an extent which makes a major difference. Mean and median are example of such statistics. By changing the extreme values we do not see a substantial difference in the value of mean and median for the data set.
Consider a sample: 1,2,3,4,4,5,6,7,8 The median for this data set is 4. If we change the extreme values to get this sample: -5,2,3,4,4,5,6,7,100 The median will still be the same i.e. 4. This is what is meant by a resistant statistic.
IQR=5+2=7 because you have to find the median and the median below the median and above the median to get 5 and a negative two and 5 subtract a negative is the same as adding a positive so then you get 7.
