np.std() and np.var() for spread in NumPy - Practice Problems & Coding Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

Output of np.std() with axis parameter

What is the output of the following code snippet?

NumPy

import numpy as np
arr = np.array([[1, 2, 3], [4, 5, 6]])
result = np.std(arr, axis=0)
print(result)

A [1.11803399 1.11803399 1.11803399]

B [2.5 2.5 2.5]

C [2.0 2.0 2.0]

D [1.5 1.5 1.5]

💡 Hint

Remember that np.std calculates the standard deviation along the specified axis.

The standard deviation along axis 0 is calculated for each column. Each column has mean 2.5, sum of squared differences 4.5, divided by 2 (ddof=0) gives variance 2.25, std = 1.5.

❓ data_output

intermediate

Variance of a 1D array

What is the output of this code?

NumPy

import numpy as np
arr = np.array([2, 4, 4, 4, 5, 5, 7, 9])
print(np.var(arr))

A 3.0

B 2.0

C 4.0

D 1.5

💡 Hint

Variance is the average of squared differences from the mean.

The variance of the array is 3.0, calculated as the average squared distance from the mean.

🔧 Debug

advanced

Identify the error in variance calculation

What error will this code raise?

NumPy

import numpy as np
arr = np.array([1, 2, 3])
result = np.var(arr, ddof=2)
print(result)

A TypeError: ddof must be an integer

B RuntimeWarning: Degrees of freedom <= 0 for slice

C No error, output is 2.0

D ValueError: ddof must be less than or equal to the number of elements

💡 Hint

Check the degrees of freedom parameter and its effect on variance calculation.

Using ddof=2 with 3 elements gives degrees of freedom = 3-2=1 >0, so no warning or error. Mean=2, sum of squared differences=2, variance=2/1=2.0.

🚀 Application

advanced

Choosing between np.std() and np.var() for data spread

You want to compare the spread of two datasets visually. Which numpy function is better to use for direct comparison and why?

A np.var(), because variance is easier to interpret visually

B np.std(), because variance can be negative

C np.var(), because it is the square root of standard deviation

D np.std(), because it gives spread in the same units as the data

💡 Hint

Think about the units of measurement for variance and standard deviation.

Standard deviation is in the same units as the data, making it easier to interpret and compare visually. Variance is squared units, which can be confusing.

🧠 Conceptual

expert

Effect of axis and ddof on np.var() output shape

Given a 3D numpy array with shape (2,3,4), what is the shape of the output when calling np.var(arr, axis=(1,2), ddof=1)?

A (2,3,4)

B (2,)

C (1,)

D (3,4)

💡 Hint

Think about how variance reduces dimensions along specified axes.

Variance computed along axes 1 and 2 reduces those dimensions, leaving axis 0 intact, so output shape is (2,).