CUMFREQ

Overview

The CUMFREQ function computes the cumulative frequency histogram of the input data by dividing it into a specified number of bins and counting the cumulative number of observations up to each bin. This is useful for understanding the distribution of values in a dataset and for identifying percentiles or cumulative counts across ranges. It is a wrapper around SciPy’s scipy.stats.cumfreq function.

This example function is provided as-is without any representation of accuracy.

Usage

To use the function in Excel:


=CUMFREQ(data, numbins, [lowerlimit], [upperlimit])

data (2D list or scalar, required): Input data to analyze, as a column vector or a single value.
numbins (integer, required): Number of bins to use for the histogram.
lowerlimit (float, optional): Lower bound for the histogram range.
upperlimit (float, optional): Upper bound for the histogram range.

The function returns a single column of cumulative counts as a 2D list, where each row corresponds to a bin.

Examples

Example 1: Default range

Inputs:

data	numbins
1	4
2
3
4

Excel formula:


=CUMFREQ({1;2;3;4}, 4)

Expected output:

Result
1
2
3
4

Example 2: Duplicate values

Inputs:

data	numbins
1	2
1
2
2

Excel formula:


=CUMFREQ({1;1;2;2}, 2)

Expected output:

Result
2
4

Example 3: More bins

Inputs:

data	numbins
1	5
2
3
4
5

Excel formula:


=CUMFREQ({1;2;3;4;5}, 5)

Expected output:

Result
1
2
3
4
5

Example 4: Custom range

Inputs:

data	numbins	lowerlimit	upperlimit
1	2	0	4
2
3

Excel formula:


=CUMFREQ({1;2;3}, 2, 0, 4)

Expected output:

Result
1
3

Python Code


from scipy.stats import cumfreq as _cumfreq
 
 
def cumfreq(data, numbins=10, lowerlimit=None, upperlimit=None):
    """
    Returns the cumulative frequency histogram for the input data.
 
    Args:
        data: 2D list or scalar of float values. Input data to analyze.
        numbins: Number of bins to use for the histogram (default 10).
        lowerlimit: Lower bound for the histogram range (optional).
        upperlimit: Upper bound for the histogram range (optional).
 
    Returns:
        2D list of cumulative counts for each bin, or an error message as a string.
 
    This example function is provided as-is without any representation of accuracy.
    """
    # Validate data
    try:
        if not isinstance(data, list):
            flat = [float(data)]
        else:
            if all(isinstance(row, list) and len(row) >= 1 for row in data):
                flat = [float(row[0]) for row in data]
            else:
                return "Invalid input: data must be a 2D list or scalar."
    except Exception:
        return "Invalid input: data must be numeric."
    # Require at least two data points
    if len(flat) < 2:
        return "Invalid input: data must contain at least two values."
    # Validate numbins
    try:
        nb = int(numbins)
        if nb <= 0:
            return "Invalid input: numbins must be a positive integer."
    except Exception:
        return "Invalid input: numbins must be an integer."
    # Validate limits
    drl = None
    if lowerlimit is not None or upperlimit is not None:
        if lowerlimit is None or upperlimit is None:
            return "Invalid input: both lowerlimit and upperlimit must be provided."
        try:
            low = float(lowerlimit)
            up = float(upperlimit)
        except Exception:
            return "Invalid input: limits must be numeric."
        drl = (low, up)
    # Compute cumulative frequency
    try:
        if drl:
            res = _cumfreq(flat, numbins=nb, defaultreallimits=drl)
        else:
            res = _cumfreq(flat, numbins=nb)
        counts = res.cumcount.tolist()
    except Exception as e:
        return f"scipy.stats.cumfreq error: {e}"
    # Convert to 2D list
    return [[c] for c in counts]

Example Workbook

Link to Workbook