Median Calculator on Matlab Without Median

What is Median?

The median is a measure of central tendency that represents the middle value in a dataset. Unlike the mean, the median is not affected by extreme values (outliers) and provides a better representation of the central position in skewed distributions.

To calculate the median:

1. Arrange all data points in numerical order.
2. If the number of observations is odd, the median is the middle number.
3. If the number of observations is even, the median is the average of the two middle numbers.

Median Formula

The median formula depends on whether the number of data points is odd or even:

This formula is implemented in the MATLAB code example below.

MATLAB Median Calculation Without median()

Here's a MATLAB function that calculates the median without using the built-in median() function:

function m = customMedian(data)
    % Sort the data in ascending order
    sortedData = sort(data);
    n = length(sortedData);

    % Calculate median based on whether n is odd or even
    if mod(n, 2) == 1
        % Odd number of elements
        m = sortedData((n + 1)/2);
    else
        % Even number of elements
        m = (sortedData(n/2) + sortedData(n/2 + 1)) / 2;
    end
end

This function first sorts the input data and then applies the median formula based on whether the number of elements is odd or even.

Example Calculation

Let's calculate the median of the following dataset: [5, 2, 9, 1, 5, 6]

1. Sort the data: [1, 2, 5, 5, 6, 9]
2. Count the number of elements: 6 (even)
3. Calculate median: (5 + 5) / 2 = 5

The median of this dataset is 5.