trimmean
Mean, excluding outliers
Syntax
Description
m = trimmean(X,percent)X, computed after removing the outliers
of X. For example, if X is a vector that has
n values, m is the mean of X
excluding the highest and lowest k data values, where k =
n*(percent/100)/2.
If
Xis a vector, thentrimmean(X,percent)is the mean of all the values ofX, computed after removing the outliers.If
Xis a matrix, thentrimmean(X,percent)is a row vector of column means, computed after removing the outliers.If
Xis a multidimensional array, thentrimmeanoperates along the first nonsingleton dimension ofX.
m = trimmean(___,vecdim)vecdim. For example, if X is a 2-by-3-by-4 array,
then trimmean(X,10,[1 2]) returns a 1-by-1-by-4 array. Each value of the
output array is the mean of the middle 90% of the values on the corresponding page of
X.
Examples
Find the relative efficiency of the 10% trimmed mean to the sample mean for a given data set.
Generate a 100-by-100 matrix of random numbers from the standard normal distribution. This matrix represents 100 samples, each containing 100 data points.
rng default; % For reproducibility X = normrnd(0,1,100,100);
Compute the sample mean and the 10% trimmed mean for each column of the data matrix.
m = mean(X); % Sample mean trim = trimmean(X,10); % Trimmed mean
Compute the relative efficiency of the trimmed mean to the sample mean. The relative efficiency is the variance of the sample mean divided by the variance of the trimmed mean.
vm = var(m) % Variance of the sample meanvm = 0.0094
vtrim = var(trim) % Variance of the trimmed meanvtrim = 0.0097
efficiency = vm/vtrim % Relative efficiency of the trimmed mean to the sample meanefficiency = 0.9663
The sample mean has a smaller variance than the trimmed mean (efficiency < 1). Therefore, the trimmed mean is less efficient than the sample mean.
Control the trimming for a distribution with outliers when k (half the number of outliers to be trimmed) is not an integer.
Generate a vector of random numbers from the Student's t distribution with degrees of freedom equal to 1. The Student's t distribution tends to have outliers.
rng default; % For reproducibility nu = 1; % Degrees of freedom n = 60; % Number of rows m = 1; % Number of columns x = trnd(nu,n,m); % Vector
Visualize the distribution using a normal probability plot.
probplot(x)
Although the distribution is symmetric around zero, several outliers affect the mean.
Find the mean of the data.
mn = mean(x)
mn = 1.6452
Find the 33% trimmed mean of the data.
trim = trimmean(x,33)
trim = 0.4940
The 33% trimmed mean is closer to zero, which is more representative of the data. For the 33% trimmed mean, k is not an integer (k = 60*(33/100)/2 gives a value of 9.9). Therefore, trimmean rounds k to the nearest integer (10) by default.
Control trimming by rounding k down to the next smaller integer (9). Specify the control for trimming to 'floor'.
trim = trimmean(x,33,'floor')trim = 0.4933
Find the trimmed mean along different dimensions for a matrix.
Generate a matrix of random numbers from the Student's t distribution. The Student's t distribution tends to have outliers.
rng('default') nu = 1; % Degrees of freedom n = 2; % Number of rows m = 100; % Number of columns X = trnd(nu,n,m);
Visualize the distribution for each row of X using a normal probability plot.
for i = 1:n figure() probplot(X(i,:)) end
Find the mean for each row of X.
mn = mean(X,2)
mn = 2×1
-2.7379
2.0087
Find the 30% trimmed mean for each row of X. Specify dim = 2 as the operating dimension.
trim = trimmean(X,30,2)
trim = 2×1
-0.0868
0.1115
The 30% trimmed mean of each row is closer to zero, which is more representative of the data.
Calculate the trimmed mean over multiple dimensions by using the 'all' and vecdim input arguments.
Create a 5-by-4-by-2 array with some outlier values.
X = reshape(1:40,[5 4 2]); X([3 37]) = -100
X =
X(:,:,1) =
1 6 11 16
2 7 12 17
-100 8 13 18
4 9 14 19
5 10 15 20
X(:,:,2) =
21 26 31 36
22 27 32 -100
23 28 33 38
24 29 34 39
25 30 35 40
Find the 10% trimmed mean of X.
mall = trimmean(X,10,'all')mall = 19.4722
mall is the mean of the middle 90% of the values in X.
Find the 10% trimmed mean for each page of X.
mpage = trimmean(X,10,[1 2])
mpage = mpage(:,:,1) = 10.3889 mpage(:,:,2) = 29.6111
For example, mpage(1,1,2) is the mean of the middle 90% of the values in X(:,:,2).
Input Arguments
Input data that represents a sample from a population, specified as a vector, matrix, or multidimensional array.
If
Xis a vector, thentrimmean(X,percent)is the mean of all the values ofX, computed after removing the outliers.If
Xis a matrix, thentrimmean(X,percent)is a row vector of column means, computed after removing the outliers.If
Xis a multidimensional array, thentrimmeanoperates along the first nonsingleton dimension ofX.
To specify the operating dimension when X is a matrix or an
array, use the dim input argument.
trimmean treats NaN values in
X as missing values and removes them.
Data Types: single | double
Percentage of input data to be trimmed, specified as a scalar between
0 and 100.
trimmean uses the value of percent to
determine the number of outliers (highest and lowest k values in
X) to remove from X before computing the mean.
For X with n values, k =
n*(percent/100)/2.
Data Types: single | double
Control for trimming when k (half the number of outliers) is not
an integer, specified as one of the values in this table.
| Value | Description |
|---|---|
'round' | Round k to the nearest integer (round to a smaller
integer if k is a half integer). This value is the
default. |
'floor' | Round k down to the next smaller integer. |
'weighted' | If k = i + f, where i is
an integer and f is a fraction, compute a weighted mean
with weight (1 – f) for the (i + 1)th
and (n – i)th values, and full weight for the values
between them. |
Data Types: char | string
Dimension along which to operate, specified as a positive integer scalar. If you do
not specify a value, then the default value is the first array dimension of
X whose size does not equal 1.
Consider a two-dimensional array X:
If
dimis equal to 1, thentrimmean(X,percent,1)returns a row vector containing the trimmed mean for each column inX.If
dimis equal to 2, thentrimmean(X,percent,2)returns a column vector containing the trimmed mean for each row inX.
If dim is greater than ndims(X) or if
size(X,dim) is 1, then trimmean returns
X.
Data Types: single | double
Vector of dimensions, specified as a positive integer vector. Each element of
vecdim represents a dimension of the input array
X. The output m has length 1 in the
specified operating dimensions. The other dimension lengths are the same for
X and m.
For example, if X is a 2-by-3-by-3 array, then
trimmean(X,10,[1 2]) returns a 1-by-1-by-3 array. Each element of
the output is the mean of the middle 90% of the values on the corresponding page of
X.
Data Types: single | double
Output Arguments
Tips
The trimmed mean is a robust estimate of the location of a data sample. If the data contains outliers, then the trimmed mean represents the center of the data better than the sample mean. However, if all the data is from the same probability distribution, then the trimmed mean is less efficient than the sample mean as an estimator of the data location.
