Histogram computation with np.histogram() in NumPy - Step-by-Step Execution

Concept Flow - Histogram computation with np.histogram()

Input data array

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Choose number of bins or bin edges

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np.histogram() computes counts per bin

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Return counts and bin edges

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Use counts for analysis or plotting

The data array is divided into bins, counts of values per bin are computed, and both counts and bin edges are returned.

Execution Sample

NumPy

import numpy as np

values = np.array([1, 2, 2, 3, 4, 5, 5, 5])
counts, bins = np.histogram(values, bins=4)
print(counts, bins)

This code counts how many values fall into each of 4 bins for the given array.

Execution Table

Step	Action	Data/Condition	Result
1	Input array	[1, 2, 2, 3, 4, 5, 5, 5]	Array ready for histogram
2	Set bins	bins=4	4 equal-width bins from min=1 to max=5
3	Calculate bin edges	Range 1 to 5	Edges: [1.0, 2.0, 3.0, 4.0, 5.0]
4	Count values in bins	Bin 1: [1.0, 2.0)	Count = 1 (value 1)
5	Count values in bins	Bin 2: [2.0, 3.0)	Count = 2 (values 2,2)
6	Count values in bins	Bin 3: [3.0, 4.0)	Count = 1 (value 3)
7	Count values in bins	Bin 4: [4.0, 5.0]	Count = 1 (value 4)
8	Count values equal to max	Value 5	Count = 3 (values 5,5,5) added to last bin
9	Return results	counts and bins arrays	counts=[1,2,1,4], bins=[1.,2.,3.,4.,5.]
10	Print output	counts and bins	[1 2 1 4] [1. 2. 3. 4. 5.]

💡 All values counted into bins; histogram computation complete

Variable Tracker

Variable	Start	After Step 3	After Step 9
values	[1,2,2,3,4,5,5,5]	[1,2,2,3,4,5,5,5]	[1,2,2,3,4,5,5,5]
bins	None	[1.0, 2.0, 3.0, 4.0, 5.0]	[1.0, 2.0, 3.0, 4.0, 5.0]
counts	None	None	[1, 2, 1, 4]

Key Moments - 2 Insights

Why does the last bin count include values equal to the max edge?

np.histogram includes values equal to the rightmost edge in the last bin, as shown in step 8 and 9 where values 5 are counted in the last bin.

Why are the bins edges one more than the counts length?

Bins define edges, so for N bins there are N+1 edges. This is shown in step 3 and 9 where 4 bins have 5 edges.

Visual Quiz - 3 Questions

Look at the execution table at step 6, how many values fall into the third bin?

A 2

B 1

C 3

D 0

💡 Hint

Check the 'Count values in bins' action for Bin 3 in step 6

At which step does np.histogram finalize the counts array?

A Step 9

B Step 7

C Step 4

D Step 10

💡 Hint

Look for the step where counts array is assigned and returned

If the bins parameter was changed from 4 to 2, how would the counts array length change?

A It would have length 3

B It would have length 4

C It would have length 2

D It would have length 5

💡 Hint

Recall that counts length = number of bins, and bins edges length = bins + 1

Concept Snapshot

np.histogram(data, bins)
- Divides data into bins
- Returns counts per bin and bin edges
- Counts length = bins count
- Last bin includes values equal to max edge
- Useful for data distribution analysis

Full Transcript

This visual trace shows how np.histogram works step-by-step. First, the input array is ready. Then, the number of bins is set, here 4. The function calculates bin edges from the minimum to maximum value. It counts how many values fall into each bin interval. Values equal to the maximum edge are included in the last bin. Finally, counts and bin edges arrays are returned and printed. This helps understand how data is grouped into ranges for analysis.