KDE overlay concept in Matplotlib - Practice Problems & Coding Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

What is the output of this KDE overlay plot code?

Look at the code below that creates two KDE plots overlaid on the same axes. What will the plot show?

Matplotlib

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

np.random.seed(0)
data1 = np.random.normal(0, 1, 100)
data2 = np.random.normal(2, 1, 100)

kde1 = gaussian_kde(data1)
kde2 = gaussian_kde(data2)

x = np.linspace(-4, 6, 200)

plt.plot(x, kde1(x), label='Data 1')
plt.plot(x, kde2(x), label='Data 2')
plt.legend()
plt.show()

A Two smooth curves showing peaks near 0 and 2, overlapping slightly

B Two flat lines with no peaks

C A single curve with one peak at 1

D Two curves with peaks at -2 and 4

💡 Hint

Think about where the normal distributions are centered and how KDE estimates density.

The code generates two normal distributions centered at 0 and 2. The KDE plots show smooth density curves with peaks near these centers, overlapping because the distributions are close.

❓ data_output

intermediate

How many peaks are visible in the KDE overlay plot?

Given two datasets with different centers, when overlaid using KDE plots, how many distinct peaks should appear?

Matplotlib

import numpy as np
from scipy.stats import gaussian_kde

np.random.seed(1)
data1 = np.random.normal(-1, 0.5, 150)
data2 = np.random.normal(3, 0.5, 150)

kde1 = gaussian_kde(data1)
kde2 = gaussian_kde(data2)

x = np.linspace(-3, 5, 300)

kde_values1 = kde1(x)
kde_values2 = kde2(x)

combined = kde_values1 + kde_values2

peaks = ((combined[1:-1] > combined[:-2]) & (combined[1:-1] > combined[2:])).sum()

A 1

B 0

C 3

D 2

💡 Hint

Each dataset is centered far apart, so each should create a peak.

Since the two datasets are centered at -1 and 3, their KDEs produce two distinct peaks in the combined density.

❓ visualization

advanced

Which option correctly overlays KDE plots with different bandwidths?

You want to overlay KDE plots of two datasets but use a smaller bandwidth for the second dataset to get a sharper curve. Which code snippet does this correctly?

A

kde1 = gaussian_kde(data1, bw_method='scott')
kde2 = gaussian_kde(data2, bw_method='silverman')

B

kde1 = gaussian_kde(data1, bw_method=0.1)
kde2 = gaussian_kde(data2, bw_method=0.5)

C

kde1 = gaussian_kde(data1, bw_method=0.5)
kde2 = gaussian_kde(data2, bw_method=0.1)

D

kde1 = gaussian_kde(data1)
kde2 = gaussian_kde(data2, bw_method=0.1)

💡 Hint

Smaller bandwidth means sharper peaks. Assign smaller bandwidth to second dataset.

Option C sets a larger bandwidth (0.5) for the first dataset and a smaller bandwidth (0.1) for the second, producing a sharper KDE curve for the second dataset as requested.

🔧 Debug

advanced

What error does this KDE overlay code raise?

This code tries to overlay KDE plots but raises an error. What is the error?

Matplotlib

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

np.random.seed(0)
data1 = np.random.normal(0, 1, 100)
data2 = []

kde1 = gaussian_kde(data1)
kde2 = gaussian_kde(data2)

x = np.linspace(-4, 4, 100)

plt.plot(x, kde1(x), label='Data 1')
plt.plot(x, kde2(x), label='Data 2')
plt.legend()
plt.show()

A TypeError: 'list' object is not callable

B ValueError: `dataset` input should have shape (n, m) with n>1

C NameError: name 'gaussian_kde' is not defined

D IndexError: index out of range

💡 Hint

Check the shape and content of data2 before passing to gaussian_kde.

The second dataset is empty, so gaussian_kde raises a ValueError because it needs at least one data point to estimate density.

🚀 Application

expert

How to combine and visualize KDE overlays for three datasets with different colors and transparency?

You have three datasets and want to plot their KDE overlays on the same plot. You want each KDE curve to have a distinct color and some transparency so overlaps are visible. Which code snippet achieves this?

A

plt.plot(x, kde1(x), color='red', alpha=0.5)
plt.plot(x, kde2(x), color='green', alpha=0.5)
plt.plot(x, kde3(x), color='blue', alpha=0.5)

B

plt.plot(x, kde1(x), alpha=0.5)
plt.plot(x, kde2(x), alpha=0.5)
plt.plot(x, kde3(x), alpha=0.5)

C

plt.plot(x, kde1(x), color='red')
plt.plot(x, kde2(x), color='green')
plt.plot(x, kde3(x), color='blue')

D

plt.plot(x, kde1(x), color='red', alpha=1)
plt.plot(x, kde2(x), color='red', alpha=0.5)
plt.plot(x, kde3(x), color='red', alpha=0.3)

💡 Hint

Use both color and alpha parameters in plt.plot for distinct colors and transparency.

Option A sets distinct colors and alpha=0.5 for transparency, making overlaps visible and curves distinguishable.