Scalar operations on arrays in NumPy - Cheat Sheet & Quick Revision

Recall & Review

beginner

What happens when you add a scalar to a NumPy array?

The scalar is added to each element of the array individually. This is called broadcasting.

beginner

How does multiplying a NumPy array by a scalar affect the array?

Each element in the array is multiplied by the scalar, scaling all values by that number.

beginner

What is the result of subtracting a scalar from a NumPy array?

The scalar is subtracted from each element of the array, reducing each value by that scalar.

beginner

Can you divide a NumPy array by a scalar? What happens?

Yes, dividing a NumPy array by a scalar divides each element by that scalar, scaling down the values.

intermediate

Why are scalar operations on arrays useful in data science?

They allow quick and easy element-wise transformations on datasets without writing loops, making code simpler and faster.

What does adding a scalar to a NumPy array do?

A Adds the scalar to the array shape

B Adds the scalar only to the first element

C Adds the scalar to each element of the array

D Throws an error

Adding a scalar to a NumPy array adds that scalar to every element individually.

If you multiply a NumPy array by 0, what is the result?

A An error occurs

B The array remains unchanged

C Each element doubles

D Each element becomes 0

Multiplying by 0 sets every element in the array to 0.

Which operation scales all elements of a NumPy array by the same number?

A Adding a scalar

B Multiplying by a scalar

C Changing the array shape

D Subtracting a scalar

Multiplying by a scalar scales all elements by that number.

What happens if you divide a NumPy array by 1?

A Each element is divided by 1, so the array stays the same

B Each element becomes 1

C Each element doubles

D An error occurs

Dividing by 1 leaves each element unchanged.

Why are scalar operations on arrays preferred over loops in NumPy?

A They are faster and use less code

B They are slower but easier to write

C They require more memory

D They only work on 1D arrays

Scalar operations use optimized code internally, making them faster and simpler than loops.

Explain how scalar addition works on a NumPy array and why it is useful.

Think about how adding one number affects every item in a list.

Describe the effect of multiplying a NumPy array by a scalar and give a real-life example.

Imagine increasing all prices by 10%.

Practice

1. What happens when you add a scalar value to a NumPy array?
arr = np.array([1, 2, 3])
result = arr + 5

easy

A. 5 is added only to the first element

B. The array becomes a scalar value 5

C. 5 is added to each element of the array

D. An error occurs because you cannot add a scalar to an array

Solution

1. Step 1: Understand scalar addition on arrays

   Adding a scalar to a NumPy array adds that scalar to every element individually.

2. Step 2: Apply addition to each element

   Each element in [1, 2, 3] gets 5 added, resulting in [6, 7, 8].

3. Final Answer:

   5 is added to each element of the array -> Option C

4. Quick Check:

   Scalar + array = element-wise addition [OK]

Hint: Scalar operations apply to every element individually [OK]

Common Mistakes:

• Thinking scalar adds only to first element
• Expecting an error when adding scalar
• Confusing scalar with array addition

2. Which of the following is the correct syntax to multiply every element of a NumPy array arr by 3?

easy

A. arr * 3

B. arr * [3]

C. arr * arr[3]

D. arr * (3,)

Solution

1. Step 1: Identify scalar multiplication syntax

   Multiplying an array by a scalar uses the * operator with a number, like arr * 3.

2. Step 2: Check other options

   arr * [3] tries to multiply by a list, arr * arr[3] accesses an element (may cause error if index out of range), arr * (3,) is a tuple, not scalar.

3. Final Answer:

   arr * 3 -> Option A

4. Quick Check:

   Scalar multiplication uses * scalar [OK]

Hint: Use * with a number, not list or tuple [OK]

Common Mistakes:

• Using list or tuple instead of scalar
• Accessing array element incorrectly
• Confusing scalar with array

3. What is the output of the following code?

import numpy as np
arr = np.array([2, 4, 6])
result = arr - 1
print(result)

medium

A. [3 5 7]

B. [1 3 5]

C. [2 4 6]

D. Error: unsupported operand

Solution

1. Step 1: Understand scalar subtraction on array

   Subtracting 1 from each element in [2, 4, 6] results in [1, 3, 5].

2. Step 2: Confirm output matches expected array

   The print statement outputs the array as [1 3 5] without commas.

3. Final Answer:

   [1 3 5] -> Option B

4. Quick Check:

   Array - scalar subtracts from each element [OK]

Hint: Subtract scalar from each element for result [OK]

Common Mistakes:

• Expecting commas in printed array
• Adding instead of subtracting
• Thinking operation causes error

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

import numpy as np
arr = np.array([1, 2, 3])
result = arr + '5'
print(result)

medium

A. Cannot add string scalar to numeric array

B. Array is not defined

C. Missing import statement

D. Syntax error in addition

Solution

1. Step 1: Identify data types involved in addition

   arr is numeric array, '5' is a string scalar. NumPy cannot add string to numbers.

2. Step 2: Understand error cause

   Adding string to numeric array causes TypeError because types mismatch.

3. Final Answer:

   Cannot add string scalar to numeric array -> Option A

4. Quick Check:

   Scalar type must match array type [OK]

Hint: Scalar must be number, not string, for numeric arrays [OK]

Common Mistakes:

• Thinking import is missing
• Confusing syntax error with type error
• Assuming array is undefined

5. You have a NumPy array arr = np.array([10, 20, 30, 40]). You want to reduce each element by 10% using scalar operations. Which code correctly does this?

hard

A. arr + 0.9

B. arr - 0.1

C. arr / 10

D. arr * 0.9

Solution

1. Step 1: Understand reducing by 10%

   Reducing by 10% means multiplying by 90% or 0.9.

2. Step 2: Apply scalar multiplication

   Multiplying arr by 0.9 scales each element down by 10%.

3. Step 3: Check other options

   Subtracting 0.1 reduces by fixed amount, dividing by 10 reduces by 90%, adding 0.9 increases values.

4. Final Answer:

   arr * 0.9 -> Option D

5. Quick Check:

   Multiply by 0.9 to reduce by 10% [OK]

Hint: Multiply by 0.9 to reduce by 10% [OK]

Common Mistakes:

• Subtracting 0.1 instead of 10%
• Dividing instead of multiplying
• Adding instead of reducing