SciPy with Matplotlib for visualization - Practice Problems & Coding Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

Output of a Gaussian distribution plot code

What will be the output of this code snippet that plots a Gaussian distribution using SciPy and Matplotlib?

SciPy

import numpy as np
import matplotlib.pyplot as plt
from scipy.stats import norm

x = np.linspace(-3, 3, 100)
y = norm.pdf(x, 0, 1)
plt.plot(x, y)
plt.title('Gaussian Distribution')
plt.xlabel('x')
plt.ylabel('Probability Density')
plt.show()

A A bar chart with bars increasing from left to right

B A horizontal line at y=1 across the x-axis range

C A line plot showing a bell-shaped curve centered at 0

D A scatter plot with random points scattered around zero

💡 Hint

Think about what the probability density function of a normal distribution looks like.

The code uses norm.pdf to compute the probability density function of a normal distribution centered at 0 with standard deviation 1. Plotting this produces a bell-shaped curve.

❓ data_output

intermediate

Resulting array from SciPy interpolation

Given the following code using SciPy's interp1d, what is the output array printed?

SciPy

import numpy as np
from scipy.interpolate import interp1d

x = np.array([0, 1, 2, 3])
y = np.array([0, 1, 4, 9])
f = interp1d(x, y)
print(f([1.5, 2.5]))

A [2.5 6.5]

B [1.5 2.5]

C [3.0 7.0]

D [1.0 4.0]

💡 Hint

Interp1d does linear interpolation between points.

At 1.5, linear interpolation between y=1 at x=1 and y=4 at x=2 gives 2.5. At 2.5, between y=4 at x=2 and y=9 at x=3 gives 6.5.

❓ visualization

advanced

Identify the plot type from SciPy clustering output

This code performs hierarchical clustering and plots a dendrogram. What does the plot visually represent?

SciPy

import numpy as np
from scipy.cluster.hierarchy import dendrogram, linkage
import matplotlib.pyplot as plt

np.random.seed(0)
data = np.random.rand(5, 2)
linked = linkage(data, 'single')
dendrogram(linked, labels=['A', 'B', 'C', 'D', 'E'])
plt.title('Hierarchical Clustering Dendrogram')
plt.show()

A A heatmap of pairwise distances

B A scatter plot of the original data points

C A bar chart showing cluster sizes

D A tree diagram showing how data points cluster step-by-step

💡 Hint

Dendrograms show hierarchical relationships between clusters.

The dendrogram visually shows the order and distance at which data points are merged into clusters.

🔧 Debug

advanced

Identify the error in SciPy curve fitting code

What error will this code raise when run?

SciPy

import numpy as np
from scipy.optimize import curve_fit

def model(x, a, b):
    return a * x + b

xdata = np.array([1, 2, 3, 4])
ydata = np.array([2, 4, 6, 8])

params, covariance = curve_fit(model, xdata, ydata, p0=[1])

A No error, code runs successfully

B ValueError: p0 must be of length 2 for two parameters

C RuntimeWarning: overflow encountered in multiply

D TypeError: model() missing 1 required positional argument

💡 Hint

Check the initial guess p0 length matches the number of parameters in the model.

The model function has two parameters (a, b), but p0 is given as a list with one element. curve_fit expects p0 length to match parameter count.

🚀 Application

expert

Choosing the correct SciPy function for statistical test visualization

You want to visualize the distribution of two independent samples and test if they come from the same distribution using SciPy and Matplotlib. Which approach below correctly combines the test and visualization?

A Use scipy.stats.ks_2samp to test, then plot both samples' histograms with plt.hist

B Use scipy.stats.ttest_ind to test, then plot a scatter plot of the samples

C Use scipy.stats.chisquare to test, then plot a line plot of sample means

D Use scipy.stats.pearsonr to test, then plot a bar chart of correlation coefficients

💡 Hint

The Kolmogorov-Smirnov test compares distributions; histograms show distributions visually.

ks_2samp tests if two samples come from the same distribution. Plotting histograms helps visualize their distribution shapes.