Winsorized mean is a method of averaging, a formulae with the help you which you can calculate the mean from the given values in experiment. What makes it different from Arithmatic mean is in this method, smallest and largest value around the given value in observation is removed or eliminated.
This is done to remove the effects of abnormal extreme high or low values from the calculation or final result.
After removing the values, just by arithmatic mean formulae you can calculate the Winsorized mean.
Keypoints from the blog
- Major takeaway from the blog
- Formulae for the winsorised mean
- What does this value tell you?
- Example of Winsorized mean?
1. Major takeaway from the blog
- Winsorized mean is nor arithmatic mean niether trimmed mean but gives value somewhat similar to both of them.
- It is a method of averaging which takes into account, removing of the highest and lowest abnormal extreme values from the given value of observation. After that following the same method as arithmatic mean to get the final result.
- This value is not same as trimmed mean as it involves removing of data points rather than replacing them.
2. Formulae for the winsorised mean
By below formulae , you can calculate the winsorized mean :
It is expressed in two ways. A “Sn" winsorized mean refers to the replacement of “S” smallest and largest observations, here S is an integer. Second representation is “S%”. This means removing a given percentage of values from both the ends of the data.
3. What does this value tell you?
This value is less sesitive to largest or lowest points since it is least susceptible to them. It also bring some bias in the results since already few figures are replaced.
Although it give more better figure for the analyzers than the arithmetic mean itselt. Make sure if the values are having higher gap, it will hardly make any difference calculating this value as it won’t benefit much.
4. Example of Winsorized mean?
Let’s take an example, we have to calculate winsorized mean of following data set : 1, 4, 5, 6, 7, 12, 14, 15, 21, 34. If we assume the mean is in the first order, we have to replace lowest and highest value from the data set.
It gives us 4, 5, 6, 7, 12, 14, 15, 21. Now if we calculate arithmatic mean of derived data set i.e., ( 4+5+6+7+12+14+15+21 divided by 8 ) we get trimmed mean ( Since we removed the value ) which is 10.5. It is not 11.9 as we removed the effect of 34, the largest value of data set.
Now in same example if we need to calculate winsorized mean, data set would become ( 5, 5, 5, 6, 7, 12, 14, 15, 15, 15) Instead of removing the value we replaced lowest and highest value by 2 values ahead of them. This gives mean value 9.9 which is lesser then previous one.
This is how you can calculate winsorized mean, hope you got to learn the best from this one. Stay tuned for more upcoming valuable blogs.