Cumulative histograms in Matplotlib - Step-by-Step Execution

Concept Flow - Cumulative histograms

Start with data array

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Calculate histogram bins

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Count data points per bin

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Calculate cumulative sum of counts

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Plot cumulative histogram

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End

The flow shows how data is binned, counts are accumulated cumulatively, and then plotted as a cumulative histogram.

Execution Sample

Matplotlib

import matplotlib.pyplot as plt
import numpy as np

data = np.array([1,2,2,3,4,5,5,5,6])
plt.hist(data, bins=6, cumulative=True)
plt.show()

This code plots a cumulative histogram of the data array with 6 bins.

Execution Table

Step	Data Points Processed	Bin Edges	Counts per Bin	Cumulative Counts	Plot Action
1	[]	[1.0, 1.83, 2.67, 3.5, 4.33, 5.17, 6.0]	[0, 0, 0, 0, 0, 0]	[0, 0, 0, 0, 0, 0]	Initialize bins and counts
2	[1]	[1.0, 1.83, 2.67, 3.5, 4.33, 5.17, 6.0]	[1, 0, 0, 0, 0, 0]	[1, 0, 0, 0, 0, 0]	Count 1 in first bin
3	[1,2,2]	[1.0, 1.83, 2.67, 3.5, 4.33, 5.17, 6.0]	[1, 2, 0, 0, 0, 0]	[1, 3, 3, 3, 3, 3]	Count two 2s in second bin, cumulative sums updated
4	[1,2,2,3]	[1.0, 1.83, 2.67, 3.5, 4.33, 5.17, 6.0]	[1, 2, 1, 0, 0, 0]	[1, 3, 4, 4, 4, 4]	Count 3 in third bin, cumulative sums updated
5	[1,2,2,3,4]	[1.0, 1.83, 2.67, 3.5, 4.33, 5.17, 6.0]	[1, 2, 1, 1, 0, 0]	[1, 3, 4, 5, 5, 5]	Count 4 in fourth bin, cumulative sums updated
6	[1,2,2,3,4,5,5,5]	[1.0, 1.83, 2.67, 3.5, 4.33, 5.17, 6.0]	[1, 2, 1, 1, 3, 0]	[1, 3, 4, 5, 8, 8]	Count three 5s in fifth bin, cumulative sums updated
7	[1,2,2,3,4,5,5,5,6]	[1.0, 1.83, 2.67, 3.5, 4.33, 5.17, 6.0]	[1, 2, 1, 1, 3, 1]	[1, 3, 4, 5, 8, 9]	Count 6 in last bin, cumulative sums updated
8	All data processed	[1.0, 1.83, 2.67, 3.5, 4.33, 5.17, 6.0]	[1, 2, 1, 1, 3, 1]	[1, 3, 4, 5, 8, 9]	Plot cumulative histogram and show

💡 All data points counted and cumulative sums calculated; histogram plotted.

Variable Tracker

Variable	Start	After 1	After 2	After 3	After 4	After 5	After 6	After 7	Final
data processed	[]	[1]	[1,2,2]	[1,2,2,3]	[1,2,2,3,4]	[1,2,2,3,4,5,5,5]	[1,2,2,3,4,5,5,5,6]	[1,2,2,3,4,5,5,5,6]	[1,2,2,3,4,5,5,5,6]
counts per bin	[0,0,0,0,0,0]	[1,0,0,0,0,0]	[1,2,0,0,0,0]	[1,2,1,0,0,0]	[1,2,1,1,0,0]	[1,2,1,1,3,0]	[1,2,1,1,3,1]	[1,2,1,1,3,1]	[1,2,1,1,3,1]
cumulative counts	[0,0,0,0,0,0]	[1,0,0,0,0,0]	[1,3,3,3,3,3]	[1,3,4,4,4,4]	[1,3,4,5,5,5]	[1,3,4,5,8,8]	[1,3,4,5,8,9]	[1,3,4,5,8,9]	[1,3,4,5,8,9]

Key Moments - 2 Insights

Why do cumulative counts keep increasing even if some bins have zero counts?

Because cumulative counts add all previous bin counts, zeros do not reduce the sum but keep it the same, as shown in execution_table rows 5 and 6.

Why does the last bin count increase when data points equal the upper edge?

Matplotlib includes the right edge in the last bin, so data points equal to the max value fall into the last bin, as seen in step 7 of execution_table.

Visual Quiz - 3 Questions

Look at the execution_table at step 3, what is the cumulative count for the second bin?

A 1

B 3

C 2

D 4

💡 Hint

Check the 'Cumulative Counts' column at step 3 in execution_table.

At which step does the cumulative count for the last bin first increase?

A Step 4

B Step 5

C Step 7

D Step 6

💡 Hint

Look at the 'Cumulative Counts' column for the last bin in execution_table rows.

If the data array had no values equal to 6, how would the final cumulative count for the last bin change?

A It would be 4 instead of 9

B It would be 5 instead of 9

C It would remain 9

D It would be 0

💡 Hint

Refer to variable_tracker for counts per bin and consider the last bin counts.

Concept Snapshot

Cumulative histograms count data points in bins and add counts cumulatively.
Use plt.hist(data, bins, cumulative=True) to plot.
Bins divide data range; cumulative sums show running totals.
Useful to see distribution accumulation over range.

Full Transcript

This visual execution traces how a cumulative histogram is created using matplotlib. Starting with a data array, bins are defined to split the data range. Each data point is counted into its bin. Then counts are summed cumulatively from the first bin to the last. The cumulative counts are plotted as a histogram that shows how data accumulates across bins. The execution table shows each step of counting and summing. The variable tracker follows how counts and cumulative sums change after processing each data point. Key moments clarify why cumulative sums increase even with zero counts in some bins and why the last bin includes the maximum data value. The quiz questions test understanding of cumulative counts at specific steps and effects of data changes. The snapshot summarizes the concept and usage in a few lines.