Histogram computation with np.histogram() in NumPy

Introduction

A histogram helps us see how data is spread out by counting how many values fall into different ranges.

You want to understand the distribution of exam scores in a class.

You need to check how many customers bought products in different price ranges.

You want to see the frequency of different ages in a survey.

You want to visualize how often certain temperature ranges occur in a month.

Syntax

NumPy

numpy.histogram(data, bins=10, range=None, density=False, weights=None, cumulative=False)

data: The list or array of numbers you want to analyze.

bins: How many groups (bars) you want to split your data into. Default is 10.

Examples

This splits the data into 3 groups and counts how many numbers fall into each group.

NumPy

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

Here, bins are set by specific edges: 0 to 2, 2 to 4, and 4 to 6.

NumPy

counts, bin_edges = np.histogram(data, bins=[0, 2, 4, 6])

This returns the probability density instead of counts, useful for comparing different sized datasets.

NumPy

counts, bin_edges = np.histogram(data, density=True)

Sample Program

This code counts how many ages fall into 4 groups and shows the edges of these groups.

NumPy

import numpy as np

# Sample data: ages of 10 people
ages = np.array([22, 25, 27, 30, 22, 24, 29, 31, 35, 40])

# Compute histogram with 4 bins
counts, bin_edges = np.histogram(ages, bins=4)

print('Counts:', counts)
print('Bin edges:', bin_edges)

Important Notes

The bin_edges array shows the boundaries of each group.

The number of counts is always one less than the number of bin edges.

If you want to plot the histogram, you can use matplotlib.pyplot.hist() which does this internally.

Summary

Histograms count how many data points fall into different ranges.

Use np.histogram() to get counts and bin edges separately.

You can control the number or exact edges of bins to see data distribution clearly.

Practice

1. What does the np.histogram() function in NumPy do?

easy

A. It creates a line plot of the data points.

B. It sorts the data points in ascending order.

C. It counts how many data points fall into specified bins and returns counts and bin edges.

D. It calculates the mean and median of the data points.

Solution

1. Step 1: Understand the purpose of np.histogram()

   The function divides data into bins and counts how many points fall into each bin.

2. Step 2: Identify the output of np.histogram()

   It returns two arrays: one with counts per bin and one with the bin edges.

3. Final Answer:

   It counts how many data points fall into specified bins and returns counts and bin edges. -> Option C

4. Quick Check:

   np.histogram() = counts and edges [OK]

Hint: np.histogram() returns counts and bin edges separately [OK]

Common Mistakes:

• Thinking np.histogram() sorts data
• Confusing histogram with mean calculation
• Expecting a plot from np.histogram()

2. Which of the following is the correct way to call np.histogram() to create 4 bins for data array data?

easy

A. np.histogram(data, bins=4)

B. np.histogram(4, data)

C. np.histogram(bins=data, 4)

D. np.histogram(data, bins=[4])

Solution

1. Step 1: Check the correct parameter usage for bins

   The bins parameter can be passed as a keyword argument like bins=4.

2. Step 2: Identify the correct syntax

   np.histogram(data, bins=4) is the standard and clear way to specify 4 bins.

3. Final Answer:

   np.histogram(data, bins=4) -> Option A

4. Quick Check:

   Use bins=4 to specify number of bins [OK]

Hint: Use bins=number to set bin count in np.histogram() [OK]

Common Mistakes:

• Passing bins as a list with one number
• Swapping argument order incorrectly
• Using positional argument without data first

3. What is the output of this code?

import numpy as np
data = np.array([1, 2, 2, 3, 4, 5])
counts, bins = np.histogram(data, bins=[1, 3, 5])
print(counts)

medium

A. [2 4]

B. [3 3]

C. [1 5]

D. [3 2]

Solution

1. Step 1: Understand bins and data distribution

   Bins are [1, 3) and [3, 5). Count how many data points fall into each bin.

2. Step 2: Count data points in each bin

   Bin [1,3) includes 1, 2, 2 -> 3 points; Bin [3,5) includes 3, 4 -> 2 points. Note that 5 equals the rightmost bin edge and is included in the last bin.

3. Final Answer:

   [3 3] -> Option B

4. Quick Check:

   Counts per bin = [3, 3] [OK]

Hint: Count points in each bin range carefully [OK]

Common Mistakes:

• Including right edge in left bin
• Miscounting repeated values
• Confusing bin edges with counts

4. The following code throws an error. What is the problem?

import numpy as np
data = [1, 2, 3, 4]
counts, bins = np.histogram(data, bins='five')

medium

A. The counts and bins cannot be unpacked together.

B. The data must be a NumPy array, not a list.

C. np.histogram() requires at least 5 data points.

D. The bins parameter must be an integer or sequence, not a string.

Solution

1. Step 1: Check the bins parameter type

   bins='five' is a string, but bins must be an int or a sequence of numbers.

2. Step 2: Understand np.histogram() input requirements

   Data can be list or array, and unpacking counts and bins is valid.

3. Final Answer:

   The bins parameter must be an integer or sequence, not a string. -> Option D

4. Quick Check:

   bins must be int or sequence, not string [OK]

Hint: Bins must be int or list/array, not text [OK]

Common Mistakes:

• Thinking data must be np.array
• Assuming unpacking counts and bins is invalid
• Believing minimum data length is required

5. You have data points [0, 1, 2, 3, 4, 5, 6]. You want to create a histogram with bins of width 2 starting from 0 up to 6 (inclusive). Which bins parameter should you pass to np.histogram() to get correct bin counts?

hard

A. [0, 2, 4, 6, 8]

B. [0, 2, 4, 6]

C. 3

D. [0, 1, 2, 3, 4, 5, 6]

Solution

1. Step 1: Determine bin edges for width 2 from 0 to 6 inclusive

   Bins should cover ranges: 0-2, 2-4, 4-6, and include 6, so edges are [0, 2, 4, 6, 8].

2. Step 2: Understand np.histogram bin edge behavior

   Rightmost edge is inclusive for the last bin, so to include 6, bin edges must go beyond 6.

3. Final Answer:

   [0, 2, 4, 6, 8] -> Option A

4. Quick Check:

   Bin edges must cover all data points [OK]

Hint: Add one extra bin edge beyond max data to include last point [OK]

Common Mistakes:

• Using bins that exclude the max value
• Using number of bins instead of edges
• Using bin edges with wrong intervals