Counting with boolean arrays in NumPy - Cheat Sheet & Quick Revision

Recall & Review

beginner

What does a boolean array represent in numpy?

A boolean array in numpy contains True or False values, often used to mark conditions or filters on data.

beginner

How can you count the number of True values in a numpy boolean array?

You can use the np.sum() function on the boolean array because True is treated as 1 and False as 0.

intermediate

Why does np.sum() work for counting True values in a boolean array?

Because in numpy, True is equivalent to 1 and False is equivalent to 0, so summing counts how many True values exist.

intermediate

What is the difference between np.count_nonzero() and np.sum() when used on boolean arrays?

np.count_nonzero() counts all non-zero (True) elements, similar to np.sum() on boolean arrays. Both give the count of True values.

beginner

How can boolean arrays help in real-life data analysis?

Boolean arrays help filter data, count conditions met, and quickly summarize information like how many entries meet a rule.

What does np.sum() return when applied to a boolean numpy array?

A The count of True values

B The count of False values

C The sum of True and False as strings

D An error because sum can't be used on booleans

np.sum() treats True as 1 and False as 0, so it returns the count of True values.

Which numpy function can also count True values in a boolean array besides np.sum()?

A np.unique()

B np.count_nonzero()

C np.min()

D np.mean()

np.count_nonzero() counts all non-zero (True) elements in the array.

In numpy, what numeric value does False correspond to when used in calculations?

A -1

B 1

C 0

D None

False is treated as 0 in numpy numeric operations.

If you have a boolean array [True, False, True], what does np.sum() return?

A 3

B 0

C 1

D 2

There are two True values, so the sum is 2.

Why are boolean arrays useful in data science?

A They help filter and count data based on conditions

B They store large text data efficiently

C They replace all numeric data

D They slow down calculations

Boolean arrays let you quickly find and count data entries that meet specific conditions.

Explain how you can count how many values in a numpy array meet a certain condition using boolean arrays.

Think about how True and False behave as numbers in numpy.

Describe two numpy functions that can count True values in a boolean array and how they work.

Both functions treat True as a positive count.

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