Array arithmetic (element-wise) in Data Analysis Python - Cheat Sheet & Quick Revision

Recall & Review

beginner

What does element-wise arithmetic mean when working with arrays?

Element-wise arithmetic means performing operations on each pair of corresponding elements from two arrays separately, like adding or multiplying each element one by one.

beginner

How do you add two arrays element-wise in Python using NumPy?

You simply use the + operator between two NumPy arrays of the same shape, for example: array1 + array2 adds each element of array1 to the corresponding element of array2.

intermediate

What happens if you try element-wise operations on arrays of different shapes?

If the shapes are not compatible, NumPy will raise an error. But if shapes are compatible by broadcasting rules, it will perform element-wise operations by stretching the smaller array.

beginner

Show an example of element-wise multiplication of two arrays.

Example:<br><code>import numpy as np<br>a = np.array([1, 2, 3])<br>b = np.array([4, 5, 6])<br>c = a * b  # c is array([4, 10, 18])</code>

beginner

Why is element-wise array arithmetic useful in data science?

It allows fast and simple calculations on datasets, like scaling, combining, or transforming data without writing loops, making code cleaner and faster.

What does the expression array1 + array2 do in NumPy if both arrays have the same shape?

A Concatenates the two arrays

B Adds each element of array1 to the corresponding element of array2

C Multiplies each element of array1 by the corresponding element of array2

D Raises an error

When two arrays have the same shape, the + operator adds their elements one by one.

What will happen if you try to add arrays of shapes (3,) and (2,)?

A Raises a shape mismatch error

B Element-wise addition with broadcasting

C Concatenates the arrays

D Performs dot product

Arrays with incompatible shapes that cannot be broadcasted will cause an error.

Which operator is used for element-wise multiplication of two NumPy arrays?

A -

B +

C @

D *

The * operator multiplies arrays element-wise.

If a = np.array([1, 2, 3]) and b = np.array([4, 5, 6]), what is a * b?

A [5, 7, 9]

B Error

C [4, 10, 18]

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

Element-wise multiplication multiplies each pair: 1*4=4, 2*5=10, 3*6=18.

Why is element-wise arithmetic preferred over loops in data science?

A It is faster and more concise

B It requires less memory

C It is slower but easier to read

D It avoids using arrays

Element-wise operations use optimized code and avoid explicit loops, making them faster and cleaner.

Explain what element-wise arithmetic is and give an example using Python arrays.

Think about how you add or multiply numbers one by one in two lists.

Describe what happens when you try to perform element-wise operations on arrays with incompatible shapes.

Consider what happens if you try to add a list of 3 numbers to a list of 2 numbers.

Practice

1. What does element-wise addition of two arrays mean in simple terms?

easy

A. Combining the arrays end to end without any math

B. Adding each number in one array to the corresponding number in the other array

C. Multiplying each number in one array by the total sum of the other array

D. Adding all numbers in both arrays together as a single sum

Solution

1. Step 1: Understand element-wise operation

   Element-wise means doing the operation on each pair of matching positions in two arrays.

2. Step 2: Apply to addition

   For addition, each number in the first array is added to the number in the same position in the second array.

3. Final Answer:

   Adding each number in one array to the corresponding number in the other array -> Option B

4. Quick Check:

   Element-wise addition = add matching elements [OK]

Hint: Think pair by pair addition, not total sums [OK]

Common Mistakes:

• Confusing element-wise with total sum
• Thinking arrays are joined instead of added
• Mixing addition with multiplication

2. Which of the following is the correct syntax to add two NumPy arrays a and b element-wise?

easy

A. c = a + b

B. c = a.add(b)

C. c = add(a, b)

D. c = a & b

Solution

1. Step 1: Recall NumPy addition syntax

   NumPy supports element-wise addition using the + operator directly between arrays.

2. Step 2: Check options

   c = a + b uses a + b, which is correct. c = a.add(b) is invalid syntax. c = add(a, b) requires importing add function explicitly. c = a & b uses bitwise AND, not addition.

3. Final Answer:

   c = a + b -> Option A

4. Quick Check:

   Use + for element-wise addition in NumPy [OK]

Hint: Use + operator for element-wise addition in NumPy [OK]

Common Mistakes:

• Using bitwise operators instead of +
• Trying to call add as a method on array
• Forgetting to import add function if used

3. What is the output of this code?

import numpy as np
x = np.array([1, 2, 3])
y = np.array([4, 5, 6])
z = x * y
print(z)

medium

A. [4 5 6]

B. [5 7 9]

C. [4 10 18]

D. [1 2 3 4 5 6]

Solution

1. Step 1: Understand element-wise multiplication

   Multiplying two arrays with * multiplies each element in the first array by the corresponding element in the second array.

2. Step 2: Calculate each element

   1*4=4, 2*5=10, 3*6=18, so the result is [4, 10, 18].

3. Final Answer:

   [4 10 18] -> Option C

4. Quick Check:

   Element-wise multiply = multiply matching elements [OK]

Hint: Multiply arrays element by element with * operator [OK]

Common Mistakes:

• Adding instead of multiplying
• Concatenating arrays instead of multiplying
• Confusing output format with list instead of array

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

import numpy as np
x = np.array([1, 2, 3])
y = np.array([4, 5])
z = x + y
print(z)

medium

A. You forgot to convert arrays to lists first

B. You must use np.add() instead of + operator

C. The print statement syntax is incorrect

D. Arrays have different sizes, so element-wise addition is not possible

Solution

1. Step 1: Check array sizes

   Array x has 3 elements, y has 2 elements. Element-wise operations require arrays to be the same size or broadcastable.

2. Step 2: Understand error cause

   Since sizes differ and no broadcasting applies here, addition fails with a ValueError.

3. Final Answer:

   Arrays have different sizes, so element-wise addition is not possible -> Option D

4. Quick Check:

   Array sizes must match for element-wise ops [OK]

Hint: Check array lengths before element-wise operations [OK]

Common Mistakes:

• Assuming + works regardless of size
• Thinking np.add fixes size mismatch
• Blaming print syntax for error

5. You have two arrays representing daily sales for two stores:

store1 = np.array([10, 20, 30, 40])
store2 = np.array([5, 15, 25, 35])

You want to find the total sales per day by adding these arrays element-wise. Then, you want to apply a 10% tax on the total sales. Which code correctly does this?

hard

A. total = store1 + store2
final = total * 1.10
print(final)

B. total = store1 + store2
final = total + 0.10
print(final)

C. total = store1 * store2
final = total * 1.10
print(final)

D. final = (store1 + store2) / 1.10
print(final)

Solution

1. Step 1: Calculate total sales element-wise

   Add store1 and store2 arrays element-wise using + operator to get daily totals.

2. Step 2: Apply 10% tax

   Multiply the total sales array by 1.10 to add 10% tax to each day's total.

3. Final Answer:

   total = store1 + store2 final = total * 1.10 print(final) -> Option A

4. Quick Check:

   Add then multiply by 1.10 for tax [OK]

Hint: Add arrays first, then multiply by 1.10 for tax [OK]

Common Mistakes:

• Adding 0.10 instead of multiplying by 1.10
• Multiplying arrays instead of adding
• Dividing instead of multiplying for tax