Counting with boolean arrays in NumPy - Practice Problems & Coding Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

Counting True values in a boolean NumPy array

What is the output of this code snippet that counts True values in a boolean NumPy array?

NumPy

import numpy as np
arr = np.array([True, False, True, True, False])
count = np.sum(arr)
print(count)

A 4

B 2

C 5

D 3

💡 Hint

Remember that True is treated as 1 and False as 0 in NumPy when summing.

The array has three True values. Summing treats True as 1, so the sum is 3.

❓ data_output

intermediate

Counting True values along an axis in a 2D boolean array

Given this 2D boolean array, what is the output of counting True values along axis 1?

NumPy

import numpy as np
arr = np.array([[True, False, True], [False, False, True], [True, True, True]])
counts = np.sum(arr, axis=1)
print(counts)

A [1 2 3]

B [2 1 3]

C [3 1 2]

D [2 2 2]

💡 Hint

Sum along axis 1 means count True values in each row.

Row 1 has 2 True, row 2 has 1 True, row 3 has 3 True values.

🔧 Debug

advanced

Identify the error in counting True values with incorrect axis

What error does this code raise when trying to count True values along axis 2 in a 2D boolean array?

NumPy

import numpy as np
arr = np.array([[True, False], [False, True]])
count = np.sum(arr, axis=2)
print(count)

A AxisError: axis 2 is out of bounds for array of dimension 2

B TypeError: unsupported operand type(s) for +: 'bool' and 'int'

C ValueError: operands could not be broadcast together

D No error, output is [1 1]

💡 Hint

Check the dimensions of the array and the axis argument.

The array is 2D, so valid axes are 0 and 1. Axis 2 is invalid and causes AxisError.

🚀 Application

advanced

Counting values greater than a threshold using boolean arrays

Given a NumPy array of numbers, which option correctly counts how many values are greater than 10?

NumPy

import numpy as np
arr = np.array([5, 12, 7, 20, 15])
count = ???
print(count)

A np.sum(arr > 10)

B np.sum(arr >= 10)

C np.count_nonzero(arr < 10)

D np.count_nonzero(arr == 10)

💡 Hint

Create a boolean array where values are greater than 10, then sum True values.

arr > 10 creates a boolean array. Summing counts True values, which are values > 10.

🧠 Conceptual

expert

Understanding boolean array counting with np.count_nonzero vs np.sum

Which statement best describes the difference between np.count_nonzero(boolean_array) and np.sum(boolean_array) when counting True values?

A np.count_nonzero counts False values; np.sum counts True values.

B np.count_nonzero returns the total number of elements; np.sum counts only True values.

C np.count_nonzero counts True values directly; np.sum treats True as 1 and sums them, both give the same result for boolean arrays.

D np.count_nonzero returns a boolean array; np.sum returns an integer count.

💡 Hint

Think about how True and False are treated in NumPy arithmetic and counting.

Both functions count True values in boolean arrays, but np.count_nonzero counts non-zero elements, which are True, and np.sum adds True as 1.

Practice

1. What does summing a boolean array in NumPy do?
arr = np.array([True, False, True])
What is arr.sum()?

easy

A. Returns the length of the array

B. Counts how many False values are in the array

C. Counts how many True values are in the array

D. Returns an error because booleans cannot be summed

Solution

1. Step 1: Understand boolean values in NumPy

   In NumPy, True is treated as 1 and False as 0 when summed.

2. Step 2: Sum the boolean array

   Summing [True, False, True] is 1 + 0 + 1 = 2.

3. Final Answer:

   Counts how many True values are in the array -> Option C

4. Quick Check:

   True count = 2 [OK]

Hint: Sum boolean arrays to count True values quickly [OK]

Common Mistakes:

• Thinking sum counts False values
• Believing sum returns array length
• Expecting an error when summing booleans

2. Which of the following is the correct syntax to count how many elements in arr = np.array([1, 2, 3, 4]) are greater than 2 using boolean arrays?

easy

A. (arr > 2).sum()

B. arr > 2.sum()

C. arr.sum() > 2

D. arr > 2).sum()

Solution

1. Step 1: Create boolean array for condition

   arr > 2 creates a boolean array: [False, False, True, True].

2. Step 2: Sum the boolean array correctly

   We must sum the boolean array, so use parentheses: (arr > 2).sum().

3. Final Answer:

   (arr > 2).sum() -> Option A

4. Quick Check:

   Correct syntax uses parentheses [OK]

Hint: Use parentheses around condition before sum() [OK]

Common Mistakes:

• Missing parentheses causing wrong order
• Using sum() on condition without parentheses
• Confusing comparison and sum order

3. What is the output of this code?

import numpy as np
arr = np.array([5, 3, 8, 1, 6])
count = (arr % 2 == 0).sum()
print(count)

medium

A. 3

B. 0

C. 5

D. 2

Solution

1. Step 1: Create boolean array for even numbers

   arr % 2 == 0 checks which elements are even: [False, False, True, False, True].

2. Step 2: Sum True values to count evens

   Sum is 0 + 0 + 1 + 0 + 1 = 2.

3. Final Answer:

   2 -> Option D

4. Quick Check:

   Count of even numbers = 2 [OK]

Hint: Sum boolean condition to count matching elements [OK]

Common Mistakes:

• Counting odd numbers instead
• Forgetting to use parentheses
• Misunderstanding modulo operator

4. The code below is intended to count how many values in arr are less than 10, but it raises an error. What is the error and how to fix it?

import numpy as np
arr = np.array([7, 12, 5, 20])
count = arr < 10.sum()
print(count)

medium

A. Error: Missing import statement

B. Error: 10.sum() is invalid; fix by using (arr < 10).sum()

C. No error; output is boolean array

D. Error: arr < 10 is invalid; fix by using arr.sum() < 10

Solution

1. Step 1: Identify the error in expression

   10.sum() is invalid because 10 is an integer, not an array.

2. Step 2: Correct the syntax to sum boolean array

   Use parentheses to sum the boolean array: (arr < 10).sum().

3. Final Answer:

   Error: 10.sum() is invalid; fix by using (arr < 10).sum() -> Option B

4. Quick Check:

   Parentheses needed before sum() [OK]

Hint: Always put parentheses around condition before sum() [OK]

Common Mistakes:

• Calling sum() on number instead of boolean array
• Confusing comparison and sum order
• Ignoring error message details

5. Given a 2D NumPy array data = np.array([[3, 7, 2], [5, 1, 8], [6, 4, 9]]), how can you count how many elements are greater than 5 across the entire array?

hard

A. (data > 5).sum()

B. data[data > 5].count()

C. data.sum() > 5

D. np.count(data > 5)

Solution

1. Step 1: Create boolean array for elements > 5

   data > 5 creates a boolean array marking elements greater than 5.

2. Step 2: Sum True values to count elements

   Use (data > 5).sum() to count all True values in the 2D array.

3. Final Answer:

   (data > 5).sum() -> Option A

4. Quick Check:

   Sum boolean mask counts elements > 5 [OK]

Hint: Sum boolean mask over entire array to count matches [OK]

Common Mistakes:

• Using sum() on data directly
• Trying to use count() method on NumPy array
• Using non-existent np.count() function