median of grouped frequency data

Given the data below

calculate the median of the data in MATLAB

I have the code below

class_intervals = [420 430; 430 440; 440 450; 450 460; 460 470; 470 480; 480 490; 490 500];
frequencies = [336, 2112, 2336, 1074, 1553, 1336, 736, 85];

% Calculate the cumulative frequencies
cum_frequencies = cumsum(frequencies)

% Calculate the total number of observations
N = sum(frequencies);

% Find the median class (where cumulative frequency exceeds N/2)
median_class_index = find(cum_frequencies >= N/2, 1)

% Extract the lower boundary, frequency, and cumulative frequency of the class before the median class
L = class_intervals(median_class_index, 1) % lower boundary of the median class
f = frequencies(median_class_index) % frequency of the median class
if median_class_index == 1
    cf = 0; % cumulative frequency before the median class
else
    cf = cum_frequencies(median_class_index - 1) % cumulative frequency before the median class
end

% Calculate the width of the median class interval
h = class_intervals(median_class_index, 2) - class_intervals(median_class_index, 1)

% Calculate the median using the formula
median = L + ((N/2 - cf) / f) * h

However I was wondering if instead of calculating it manually is there any inbuilt function in MATLAB to calculate median of grouped data.

Answer 1

[Anurag Ojha]

Hi Nafisa

You can use 'grpstats' function in order to calculate median of a grouped data. Adding a pseudo code:

% Create a table with the class intervals and frequencies
data = table(class_intervals, frequencies, 'VariableNames', {'ClassIntervals', 'Frequencies'});

% Calculate the median using grpstats
median_data = grpstats(data, [], 'median', 'DataVars', 'ClassIntervals');

% Extract the median values
median_values = median_data.median_ClassIntervals;

% Display the median values
disp(median_values)

There is also a inbuilt 'Median' function that you can use to caluclate median.

data = [10, 20, 30, 40, 50];
median_value = median(data);
disp(median_value);

    30

Adding documentation link for your reference:

• https://www.mathworks.com/help/stats/repeatedmeasuresmodel.grpstats.html
• https://www.mathworks.com/help/matlab/ref/median.html

[NAFISA SIDDIQUI]

Hello Anurag, thank you for your answer. However when I try to run your code using 'grpstats' function

the output says

[Anurag Ojha]

Hi Nafisa

As a work around to resolve this error you could do something like this

% Define the class intervals and frequencies
class_intervals = [420 430; 430 440; 440 450; 450 460; 460 470; 470 480; 480 490; 490 500];
frequencies = [336, 2112, 2336, 1074, 1553, 1336, 736, 85];

% Step 1: Expand the dataset based on frequencies
expanded_data = [];
groups = []; % For grpstats grouping
for i = 1:length(frequencies)
    % Determine the midpoint of the interval
    midpoint = mean(class_intervals(i, :));
    % Append midpoints according to frequency
    expanded_data = [expanded_data; repmat(midpoint, frequencies(i), 1)];
    % Assign group numbers
    groups = [groups; repmat(i, frequencies(i), 1)];
end

% Step 2: (Already included in loop) Assigning each value to a group

% Step 3: Use grpstats for group-wise statistics 
group_median = grpstats(expanded_data, groups, 'median');

% Display group-wise median
disp('Group-wise median:');

Group-wise median:

disp(group_median);

   425
   435
   445
   455
   465
   475
   485
   495

% Step 4: Calculate the overall median 
overall_median = median(expanded_data);
disp(['Overall median: ', num2str(overall_median)]);

Overall median: 450

[NAFISA SIDDIQUI]

Hello anurag the code above displays

" Index exceeds the number of array elements. Index must not exceed 1."

Error in Median (line 19)

overall_median = median(expanded_data)

[Anurag Ojha]

Hi Nafisa

I am not getting this error at my end when I execute the provided code. Can you please provide the exact code that you are executing which results in this error.

[NAFISA SIDDIQUI]

Hello Anurag, it is working however when i try to use the same code in another example it gives me a wrong answer. So I tried using this example

I get the answer 27.5 using your code. However the real answer is 25.25