what is the winsorized mean 
winsorized mean is a method of averaging that initially replaces the smallest and largest values with the observations closest to them this is done to limit the effect of outliers or abnormal extreme values or outliers on the calculation after replacing the values the arithmetic mean formula is then used to calculate the winsorized mean formula for the winsorized meanwinsorized mean x n x n 1 x n 2 x n n where n the number of largest and smallest data points to be replaced by the observation closest to them n total number of data points begin aligned text winsorized mean frac x n dots x n 1 x n 2 dots x n n textbf where begin aligned n text the number of largest and smallest data text points to be replaced by the observation text closest to them end aligned n text total number of data points end aligned winsorized mean nxn xn 1 xn 2 xn where n the number of largest and smallest datapoints to be replaced by the observationclosest to them n total number of data points winsorized means are expressed in two ways a kn winsorized mean refers to the replacement of the k smallest and largest observations where k is an integer an x winsorized mean involves replacing a given percentage of values from both ends of the data the winsorized mean is achieved by replacing the smallest and largest data points then summing all the data points and dividing the sum by the total number of data points 