Histogram computation with np.histogram() in NumPy - Practice Problems & Coding Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

Output of np.histogram() with bins=6

What is the output of the following code snippet?

NumPy

import numpy as np

arr = np.array([1, 2, 2, 3, 4, 5, 5, 5, 6])
hist, bins = np.histogram(arr, bins=6)
print(hist, bins)

A [1 2 1 0 3 2] [1. 2. 3. 4. 5. 6. ]

B [1 2 1 1 3 1] [1. 2. 3. 4. 5. 6. 7. ]

C [1 2 1 1 3 2] [1. 1.83333333 2.66666667 3.5 4.33333333 5.16666667 6. ]

D [1 2 1 1 3 2] [1. 2. 3. 4. 5. 6. 7. ]

💡 Hint

Check how np.histogram divides the range into equal-width bins when bins=6.

np.histogram with bins=6 creates 6 bins between min and max values. Here, the bins are automatically calculated with equal width between 1 and 6, resulting in 6 bins with counts as shown.

❓ data_output

intermediate

Number of bins and counts with custom bins

Given the array and bins, what is the output counts array from np.histogram?

NumPy

import numpy as np

arr = np.array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])
bins = [0, 3, 6, 9]
hist, _ = np.histogram(arr, bins=bins)
print(hist)

A [3 4 3]

B [3 3 4]

C [4 3 3]

D [3 3 3]

💡 Hint

Count how many numbers fall into each bin range: [0-3), [3-6), [6-9).

The bins are [0,3), [3,6), [6,9). Values 0,1,2 fall in first bin (3 items), 3,4,5 in second (3 items), 6,7,8 in third (3 items). The value 9 is excluded as bins are half-open intervals.

🔧 Debug

advanced

Identify the error in np.histogram bin specification

What error does the following code raise?

NumPy

import numpy as np

arr = np.array([1, 2, 3, 4, 5])
bins = [5, 4, 3, 2, 1]
hist, edges = np.histogram(arr, bins=bins)

A ValueError: bins must increase monotonically.

B TypeError: bins must be an integer or sequence.

C IndexError: list index out of range.

D No error, runs successfully.

💡 Hint

Bins must be sorted in ascending order.

np.histogram requires bins to be monotonically increasing. Here bins are in descending order, so it raises a ValueError.

❓ visualization

advanced

Histogram bin edges with uneven bin widths

What are the bin edges and counts for this histogram?

NumPy

import numpy as np

arr = np.array([1, 2, 3, 4, 5, 6, 7, 8, 9])
bins = [1, 3, 6, 10]
hist, edges = np.histogram(arr, bins=bins)
print(hist, edges)

A [2 3 4] [ 1 3 6 10]

B [2 4 3] [ 1 3 6 10]

C [3 3 3] [ 1 3 6 10]

D [2 3 3] [ 1 3 6 10]

💡 Hint

Count how many values fall into each bin: [1-3), [3-6), [6-10).

Values 1 and 2 fall in first bin (2 items), 3,4,5 in second (3 items), 6,7,8,9 in third (4 items).

🚀 Application

expert

Calculate histogram and cumulative counts

Given the array, which option correctly computes the histogram counts and cumulative counts using np.histogram?

NumPy

import numpy as np

arr = np.array([2, 4, 4, 4, 5, 5, 7, 9])
bins = [0, 3, 6, 9, 12]
hist, edges = np.histogram(arr, bins=bins)
cum_counts = np.cumsum(hist)
print(hist, cum_counts)

A [1 4 2 1] [1 5 7 8]

B [1 5 1 1] [1 6 7 8]

C [2 4 1 1] [2 6 7 8]

D [1 5 2 0] [1 6 8 8]

💡 Hint

Count values in each bin and then sum counts cumulatively.

Bins: [0-3), [3-6), [6-9), [9-12). Values: 2 in first bin (1 item), 4,4,4,5,5 in second (5 items), 7 in third (1 item), 9 in fourth (1 item). Cumulative sums add counts progressively.

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