why uper bound is multiplied by 1.5?
''' Because it has been found to work fairly reliably. If the distribution is standard normal the IQR is about 1.35 so 1.5 times that is 2.025 so the area beyond a point that far from the mean is about 2.5%. But the inner fences of a box plot are 1.5 times the IQR from the quartiles. In other words they would be a distance 2.7 from the centre with tail areas of 0.0035. This is very unlikely on the assumption of normality.The percentage depends strongly on the distribution, though and the fences are designed to allow for distributions with longer tails than the normal. You should regard this as a possible outlier. You can fairly confidently regard points three times the IQR from the quartiles as outliers. So Tukey put the outer fences there
