What is Trimmed Mean Calculator?
A trimmed mean calculator is a program that calculates the mean of numerical data. Similar to the mean or median, this statistic measures central tendency by excluding certain percentages of highest and lowest values from the set.
The trimmed mean is useful in situations where data contains extreme values or outliers that could distort results if included in the calculation of the mean. By trimming these outliers, however, a more representative estimate of “typical” value in the dataset can be provided.
To use a trimmed mean calculator, the user simply inputs the trimmed sum (the sum of all data values after trimming) and how many trimmed data points were entered, and the calculator will return the trimmed mean.
Trimmed Mean Formula
The trimmed mean is a statistical measure of central tendency that is calculated by excluding a certain percentage of the highest and lowest values in a data set, and then taking the mean of the remaining values.
μ = ∑Xi / n
Where:
- μ is the trimmed mean
- ∑Xi is the sum of the trimmed data points
- n is the number of trimmed data points
Calculating the trimmed mean requires first determining how many data points need to be removed from each end of a data set. This number is typically expressed as a percentage, such as 5%, 10% or 20% depending on the nature of the dataset and analysis being conducted.
Once trimming is complete, we can calculate the sum of all remaining data points (represented by Xi). This number is divided by n to obtain the trimmed mean (m).
Here is an example of how to calculate the trimmed mean for a set of 10 data points, with the lowest and highest 20% of values trimmed:
Data set: 8, 5, 9, 2, 7, 6, 4, 3, 10, 1
- 20% of the data points to trim: 2 (rounding up from 1.8)
- The trimmed data set: 5, 9, 7, 6, 4, 3
- The trimmed sum: 34
- The number of trimmed data points: 6
- The trimmed mean: 34 / 6 = 5.67
So the trimmed mean for this example is 5.67. This value represents the “typical” value of the data set, after excluding the lowest and highest 20% of values.
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