Exercises in Machine Learning

This book contains 75+ exercises

Download, read, and practice:
arxiv.org/pdf/2206.13446

GitHub Repo: https://github.com/michaelgutmann/ml-pen-and-paper-exercises

#DataAnalytics #Python #SQL #RProgramming #DataScience #MachineLearning #DeepLearning #Statistics #DataVisualization #PowerBI #Tableau #LinearRegression #Probability #DataWrangling #Excel #AI #ArtificialIntelligence #BigData #DataAnalysis #NeuralNetworks #GAN #LearnDataScience #LLM #RAG #Mathematics #PythonProgramming  #Keras

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Topic: Python Matplotlib – From Easy to Top: Part 1 of 6: Introduction and Basic Plotting

---

### 1. What is Matplotlib?

• Matplotlib is the most widely used Python library for data visualization.

• It provides an object-oriented API for embedding plots into applications and supports a wide variety of graphs: line charts, bar charts, scatter plots, histograms, etc.

---

### 2. Installing and Importing Matplotlib

Install Matplotlib if you haven't:

pip install matplotlib

Import the main module and pyplot interface:

import matplotlib.pyplot as plt
import numpy as np

---

### 3. Plotting a Basic Line Chart

x = [1, 2, 3, 4, 5]
y = [2, 3, 5, 7, 11]

plt.plot(x, y)
plt.title("Simple Line Plot")
plt.xlabel("X Axis")
plt.ylabel("Y Axis")
plt.grid(True)
plt.show()

---

### 4. Customizing Line Style, Color, and Markers

plt.plot(x, y, color='green', linestyle='--', marker='o', label='Data')
plt.title("Styled Line Plot")
plt.xlabel("X Axis")
plt.ylabel("Y Axis")
plt.legend()
plt.show()

---

### 5. Adding Multiple Lines to a Plot

x = np.linspace(0, 10, 100)
y1 = np.sin(x)
y2 = np.cos(x)

plt.plot(x, y1, label="sin(x)", color='blue')
plt.plot(x, y2, label="cos(x)", color='red')
plt.title("Multiple Line Plot")
plt.xlabel("X Axis")
plt.ylabel("Y Axis")
plt.legend()
plt.grid(True)
plt.show()

---

### 6. Scatter Plot

Used to show relationships between two variables.

x = np.random.rand(100)
y = np.random.rand(100)

plt.scatter(x, y, color='purple', alpha=0.6)
plt.title("Scatter Plot")
plt.xlabel("X Axis")
plt.ylabel("Y Axis")
plt.show()

---

### 7. Bar Chart

categories = ['A', 'B', 'C', 'D']
values = [4, 7, 2, 5]

plt.bar(categories, values, color='skyblue')
plt.title("Bar Chart Example")
plt.xlabel("Category")
plt.ylabel("Value")
plt.show()

---

### 8. Histogram

data = np.random.randn(1000)

plt.hist(data, bins=30, color='orange', edgecolor='black')
plt.title("Histogram")
plt.xlabel("Value")
plt.ylabel("Frequency")
plt.show()

---

### 9. Saving the Plot to a File

plt.plot([1, 2, 3], [4, 5, 6])
plt.savefig("plot.png")

---

### 10. Summary

• matplotlib.pyplot is the key module for creating all kinds of plots.
• You can customize styles, add labels, titles, and legends.
• Understanding basic plots is the foundation for creating advanced visualizations.

---

Exercise

• Plot y = x^2 and y = x^3 on the same figure.
• Create a scatter plot of 100 random points.
• Create and save a histogram from a normal distribution sample of 500 points.

---

#Python #Matplotlib #DataVisualization #Plots #Charts

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Topic: Python Matplotlib – From Easy to Top: Part 2 of 6: Subplots, Figures, and Layout Management

---

### 1. Introduction to Figures and Axes

• In Matplotlib, a Figure is the entire image or window on which everything is drawn.
• An Axes is a part of the figure where data is plotted — it contains titles, labels, ticks, lines, etc.

Basic hierarchy:

* Figure ➝ contains one or more Axes
* Axes ➝ the area where the data is actually plotted
* Axis ➝ x-axis and y-axis inside an Axes

import matplotlib.pyplot as plt
import numpy as np

---

### 2. Creating Multiple Subplots using `plt.subplot()`

x = np.linspace(0, 2*np.pi, 100)
y1 = np.sin(x)
y2 = np.cos(x)

plt.subplot(2, 1, 1)
plt.plot(x, y1, label="sin(x)")
plt.title("First Subplot")

plt.subplot(2, 1, 2)
plt.plot(x, y2, label="cos(x)", color='green')
plt.title("Second Subplot")

plt.tight_layout()
plt.show()

Explanation:

* subplot(2, 1, 1) means 2 rows, 1 column, this is the first plot.
* tight_layout() prevents overlap between plots.

---

### 3. Creating Subplots with `plt.subplots()` (Recommended)

fig, axs = plt.subplots(2, 2, figsize=(8, 6))

x = np.linspace(0, 10, 100)

axs[0, 0].plot(x, np.sin(x))
axs[0, 0].set_title("sin(x)")

axs[0, 1].plot(x, np.cos(x))
axs[0, 1].set_title("cos(x)")

axs[1, 0].plot(x, np.tan(x))
axs[1, 0].set_title("tan(x)")
axs[1, 0].set_ylim(-10, 10)

axs[1, 1].plot(x, np.exp(-x))
axs[1, 1].set_title("exp(-x)")

plt.tight_layout()
plt.show()

---

### 4. Sharing Axes Between Subplots

fig, axs = plt.subplots(1, 2, sharey=True)

x = np.linspace(0, 10, 100)

axs[0].plot(x, np.sin(x))
axs[0].set_title("sin(x)")

axs[1].plot(x, np.cos(x), color='red')
axs[1].set_title("cos(x)")

plt.show()

---

### 5. Adjusting Spacing with `subplots_adjust()`

fig, axs = plt.subplots(2, 2)

fig.subplots_adjust(hspace=0.4, wspace=0.3)

---

### 6. Nested Plots Using `inset_axes`

You can add a small plot inside another:

from mpl_toolkits.axes_grid1.inset_locator import inset_axes

fig, ax = plt.subplots()
x = np.linspace(0, 10, 100)
y = np.sin(x)

ax.plot(x, y)
ax.set_title("Main Plot")

inset_ax = inset_axes(ax, width="30%", height="30%", loc=1)
inset_ax.plot(x, np.cos(x), color='orange')
inset_ax.set_title("Inset", fontsize=8)

plt.show()

---

### 7. Advanced Layout: Gridspec

import matplotlib.gridspec as gridspec

fig = plt.figure(figsize=(8, 6))
gs = gridspec.GridSpec(3, 3)

ax1 = fig.add_subplot(gs[0, :])
ax2 = fig.add_subplot(gs[1, :-1])
ax3 = fig.add_subplot(gs[1:, -1])
ax4 = fig.add_subplot(gs[2, 0])
ax5 = fig.add_subplot(gs[2, 1])

ax1.set_title("Top")
ax2.set_title("Left")
ax3.set_title("Right")
ax4.set_title("Bottom Left")
ax5.set_title("Bottom Center")

plt.tight_layout()
plt.show()

---

### 8. Summary

• Use subplot() for quick layouts and subplots() for flexibility.
• Share axes to align multiple plots.
• Use inset_axes and gridspec for custom and complex layouts.
• Always use tight_layout() or subplots_adjust() to clean up spacing.

---

### Exercise

• Create a 2x2 grid of subplots showing different trigonometric functions.
• Add an inset plot inside a sine wave chart.
• Use Gridspec to create an asymmetric layout with at least 5 different plots.

---

#Python #Matplotlib #Subplots #DataVisualization #Gridspec #LayoutManagement

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Topic: Python Matplotlib – From Easy to Top: Part 3 of 6: Plot Customization and Styling

---

### 1. Why Customize Plots?

• Customization improves readability and presentation.
• You can control everything from fonts and colors to axis ticks and legend placement.

---

### 2. Customizing Titles, Labels, and Ticks

import matplotlib.pyplot as plt
import numpy as np

x = np.linspace(0, 10, 100)
y = np.sin(x)

plt.plot(x, y)
plt.title("Sine Wave", fontsize=16, color='navy')
plt.xlabel("Time (s)", fontsize=12)
plt.ylabel("Amplitude", fontsize=12)
plt.xticks(np.arange(0, 11, 1))
plt.yticks(np.linspace(-1, 1, 5))
plt.grid(True)
plt.show()

---

### 3. Changing Line Styles and Markers

plt.plot(x, y, color='red', linestyle='--', linewidth=2, marker='o', markersize=5, label='sin(x)')
plt.title("Styled Sine Curve")
plt.legend()
plt.grid(True)
plt.show()

Common styles:

• Line styles: '-', '--', ':', '-.'
• Markers: 'o', '^', 's', '*', 'D', etc.
• Colors: 'r', 'g', 'b', 'c', 'm', 'y', 'k', etc.

---

### 4. Adding Legends

plt.plot(x, np.sin(x), label="Sine")
plt.plot(x, np.cos(x), label="Cosine")
plt.legend(loc='upper right', fontsize=10)
plt.title("Legend Example")
plt.show()

---

### 5. Using Annotations

Annotations help highlight specific points:

plt.plot(x, y)
plt.annotate('Peak', xy=(np.pi/2, 1), xytext=(2, 1.2),
             arrowprops=dict(facecolor='black', shrink=0.05))
plt.title("Annotated Peak")
plt.show()

---

### 6. Customizing Axes Appearance

fig, ax = plt.subplots()
ax.plot(x, y)

# Remove top and right border
ax.spines['top'].set_visible(False)
ax.spines['right'].set_visible(False)

# Customize axis colors and widths
ax.spines['left'].set_color('blue')
ax.spines['left'].set_linewidth(2)

plt.title("Customized Axes")
plt.show()

---

### 7. Setting Plot Limits

plt.plot(x, y)
plt.xlim(0, 10)
plt.ylim(-1.5, 1.5)
plt.title("Limit Axes")
plt.show()

---

### 8. Using Style Sheets

Matplotlib has built-in style sheets for quick beautification.

plt.style.use('ggplot')

plt.plot(x, np.sin(x))
plt.title("ggplot Style")
plt.show()

Popular styles: seaborn, fivethirtyeight, bmh, dark_background, etc.

---

### 9. Creating Grids and Minor Ticks

plt.plot(x, y)
plt.grid(True, which='both', linestyle='--', linewidth=0.5)
plt.minorticks_on()
plt.title("Grid with Minor Ticks")
plt.show()

---

### 10. Summary

• Customize everything: lines, axes, colors, labels, and grid.
• Use legends and annotations for clarity.
• Apply styles and themes for professional looks.
• Small changes improve the quality of your plots significantly.

---

### Exercise

• Plot sin(x) with red dashed lines and circle markers.
• Add a title, custom x/y labels, and set axis ranges manually.
• Apply the 'seaborn-darkgrid' style and highlight the peak with an annotation.

---

#Python #Matplotlib #Customization #DataVisualization #PlotStyling

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Topic: Python Matplotlib – From Easy to Top: Part 4 of 6: Advanced Charts – Histograms, Pie, Box, Area, and Error Bars

---

### 1. Histogram: Visualizing Data Distribution

Histograms show frequency distribution of numerical data.

import matplotlib.pyplot as plt
import numpy as np

data = np.random.randn(1000)

plt.hist(data, bins=30, color='skyblue', edgecolor='black')
plt.title("Normal Distribution Histogram")
plt.xlabel("Value")
plt.ylabel("Frequency")
plt.grid(True)
plt.show()

Customizations:

• bins=30 – controls granularity
• density=True – normalize the histogram
• alpha=0.7 – transparency

---

### 2. Pie Chart: Showing Proportions

labels = ['Python', 'JavaScript', 'C++', 'Java']
sizes = [45, 30, 15, 10]
colors = ['gold', 'lightgreen', 'lightcoral', 'lightskyblue']
explode = (0.1, 0, 0, 0)  # explode the 1st slice

plt.pie(sizes, labels=labels, colors=colors, autopct='%1.1f%%',
        startangle=140, explode=explode, shadow=True)
plt.title("Programming Language Popularity")
plt.axis('equal')  # Equal aspect ratio ensures pie is circular
plt.show()

---

### 3. Box Plot: Summarizing Distribution Stats

Box plots show min, Q1, median, Q3, max, and outliers.

data = [np.random.normal(0, std, 100) for std in range(1, 4)]

plt.boxplot(data, patch_artist=True, labels=['std=1', 'std=2', 'std=3'])
plt.title("Box Plot Example")
plt.grid(True)
plt.show()

Tip: Use vert=False to make a horizontal boxplot.

---

### 4. Area Chart: Cumulative Trends

x = np.arange(1, 6)
y1 = np.array([1, 3, 4, 5, 7])
y2 = np.array([1, 2, 4, 6, 8])

plt.fill_between(x, y1, color="skyblue", alpha=0.5, label="Y1")
plt.fill_between(x, y2, color="orange", alpha=0.5, label="Y2")
plt.title("Area Chart")
plt.xlabel("X Axis")
plt.ylabel("Y Axis")
plt.legend()
plt.show()

---

### 5. Error Bar Plot: Showing Uncertainty

x = np.arange(0.1, 4, 0.5)
y = np.exp(-x)
error = 0.1 + 0.2 * x

plt.errorbar(x, y, yerr=error, fmt='-o', color='teal', ecolor='red', capsize=5)
plt.title("Error Bar Plot")
plt.xlabel("X Axis")
plt.ylabel("Y Axis")
plt.grid(True)
plt.show()

---

### 6. Horizontal Bar Chart

langs = ['Python', 'Java', 'C++', 'JavaScript']
popularity = [50, 40, 30, 45]

plt.barh(langs, popularity, color='plum')
plt.title("Programming Language Popularity")
plt.xlabel("Popularity")
plt.show()

---

### 7. Stacked Bar Chart

labels = ['2019', '2020', '2021']
men = [20, 35, 30]
women = [25, 32, 34]

x = np.arange(len(labels))
width = 0.5

plt.bar(x, men, width, label='Men')
plt.bar(x, women, width, bottom=men, label='Women')

plt.ylabel('Scores')
plt.title('Scores by Year and Gender')
plt.xticks(x, labels)
plt.legend()
plt.show()

---

### 8. Summary

• Histograms show frequency distribution
• Pie charts are good for proportions
• Box plots summarize spread and outliers
• Area charts visualize trends over time
• Error bars indicate uncertainty in measurements
• Stacked and horizontal bars enhance categorical data clarity

---

### Exercise

• Create a pie chart showing budget allocation of 5 departments.
• Plot 3 histograms on the same figure with different distributions.
• Build a stacked bar chart for monthly expenses across 3 categories.
• Add error bars to a decaying function and annotate the max point.

---

#Python #Matplotlib #DataVisualization #AdvancedCharts #Histograms #PieCharts #BoxPlots

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Topic: Python Matplotlib – From Easy to Top: Part 5 of 6: Images, Heatmaps, and Colorbars

---

### 1. Introduction

Matplotlib can handle images, heatmaps, and color mapping effectively, making it a great tool for visualizing:

• Image data (grayscale or color)
• Matrix-like data with heatmaps
• Any data that needs a gradient of colors

---

### 2. Displaying Images with `imshow()`

import matplotlib.pyplot as plt
import numpy as np

# Create a random grayscale image
img = np.random.rand(10, 10)

plt.imshow(img, cmap='gray')
plt.title("Grayscale Image")
plt.colorbar()
plt.show()

Key parameters:

• cmap – color map (gray, hot, viridis, coolwarm, etc.)
• interpolation – for smoothing pixelation (nearest, bilinear, bicubic)

---

### 3. Displaying Color Images

import matplotlib.image as mpimg

img = mpimg.imread('example.png')  # image must be in your directory
plt.imshow(img)
plt.title("Color Image")
plt.axis('off')  # Hide axes
plt.show()

Note: Image should be PNG or JPG. For real projects, use PIL or OpenCV for more control.

---

### 4. Creating a Heatmap from a 2D Matrix

matrix = np.random.rand(6, 6)

plt.imshow(matrix, cmap='viridis', interpolation='nearest')
plt.title("Heatmap Example")
plt.colorbar(label="Intensity")
plt.xticks(range(6), ['A', 'B', 'C', 'D', 'E', 'F'])
plt.yticks(range(6), ['P', 'Q', 'R', 'S', 'T', 'U'])
plt.show()

---

### 5. Customizing Color Maps

You can reverse or customize color maps:

plt.imshow(matrix, cmap='coolwarm_r')  # Reversed coolwarm

You can also create custom color ranges using vmin and vmax:

plt.imshow(matrix, cmap='hot', vmin=0.2, vmax=0.8)

---

### 6. Using `matshow()` for Matrix-Like Data

matshow() is optimized for visualizing 2D arrays:

plt.matshow(matrix)
plt.title("Matrix View with matshow()")
plt.colorbar()
plt.show()

---

### 7. Annotating Heatmaps

fig, ax = plt.subplots()
cax = ax.imshow(matrix, cmap='plasma')

# Add text annotations
for i in range(matrix.shape[0]):
    for j in range(matrix.shape[1]):
        ax.text(j, i, f'{matrix[i, j]:.2f}', ha='center', va='center', color='white')

plt.title("Annotated Heatmap")
plt.colorbar(cax)
plt.show()

---

### 8. Displaying Multiple Images in Subplots

fig, axs = plt.subplots(1, 2, figsize=(10, 4))

axs[0].imshow(matrix, cmap='Blues')
axs[0].set_title("Blues")

axs[1].imshow(matrix, cmap='Greens')
axs[1].set_title("Greens")

plt.tight_layout()
plt.show()

---

### 9. Saving Heatmaps and Figures

plt.imshow(matrix, cmap='magma')
plt.title("Save This Heatmap")
plt.colorbar()
plt.savefig("heatmap.png", dpi=300)
plt.close()

---

### 10. Summary

• imshow() and matshow() visualize 2D data or images
• Heatmaps are great for matrix or correlation data
• Use colorbars and annotations to add context
• Customize colormaps with cmap, vmin, vmax
• Save your visualizations easily using savefig()

---

### Exercise

• Load a grayscale image using NumPy and display it.
• Create a 10×10 heatmap with annotations.
• Display 3 subplots of the same matrix using 3 different colormaps.
• Save one of the heatmaps with high resolution.

---

#Python #Matplotlib #Heatmaps #DataVisualization #Images #ColorMapping

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Topic: Python Matplotlib – From Easy to Top: Part 6 of 6: 3D Plotting, Animation, and Interactive Visuals

---

### 1. Introduction

Matplotlib supports advanced visualizations including:

• 3D plots using mpl_toolkits.mplot3d
• Animations with FuncAnimation
• Interactive plots using widgets and event handling

---

### 2. Creating 3D Plots

You need to import the 3D toolkit:

from mpl_toolkits.mplot3d import Axes3D
import matplotlib.pyplot as plt
import numpy as np

---

### 3. 3D Line Plot

fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')

z = np.linspace(0, 15, 100)
x = np.sin(z)
y = np.cos(z)

ax.plot3D(x, y, z, 'purple')
ax.set_title("3D Line Plot")
plt.show()

---

### 4. 3D Surface Plot

fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')

X = np.linspace(-5, 5, 50)
Y = np.linspace(-5, 5, 50)
X, Y = np.meshgrid(X, Y)
Z = np.sin(np.sqrt(X**2 + Y**2))

surf = ax.plot_surface(X, Y, Z, cmap='viridis')
fig.colorbar(surf)

ax.set_title("3D Surface Plot")
plt.show()

---

### 5. 3D Scatter Plot

fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')

x = np.random.rand(100)
y = np.random.rand(100)
z = np.random.rand(100)

ax.scatter(x, y, z, c=z, cmap='plasma')
ax.set_title("3D Scatter Plot")
plt.show()

---

### 6. Creating Animations

Use FuncAnimation for animated plots.

import matplotlib.animation as animation

fig, ax = plt.subplots()
x = np.linspace(0, 2*np.pi, 128)
line, = ax.plot(x, np.sin(x))

def update(frame):
    line.set_ydata(np.sin(x + frame / 10))
    return line,

ani = animation.FuncAnimation(fig, update, frames=100, interval=50)
plt.title("Sine Wave Animation")
plt.show()

---

### 7. Save Animation as a File

ani.save("sine_wave.gif", writer='pillow')

Make sure to install pillow using:

pip install pillow

---

### 8. Adding Interactivity with Widgets

import matplotlib.widgets as widgets

fig, ax = plt.subplots()
plt.subplots_adjust(left=0.1, bottom=0.25)

x = np.linspace(0, 2*np.pi, 100)
freq = 1
line, = ax.plot(x, np.sin(freq * x))

ax_slider = plt.axes([0.25, 0.1, 0.65, 0.03])
slider = widgets.Slider(ax_slider, 'Frequency', 0.1, 5.0, valinit=freq)

def update(val):
    line.set_ydata(np.sin(slider.val * x))
    fig.canvas.draw_idle()

slider.on_changed(update)
plt.title("Interactive Sine Wave")
plt.show()

---

### 9. Mouse Interaction with Events

def onclick(event):
    print(f'You clicked at x={event.xdata:.2f}, y={event.ydata:.2f}')

fig, ax = plt.subplots()
ax.plot([1, 2, 3], [4, 5, 6])
fig.canvas.mpl_connect('button_press_event', onclick)
plt.title("Click to Print Coordinates")
plt.show()

---

### 10. Summary

• 3D plots are ideal for visualizing spatial data and surfaces
• Animations help convey dynamic changes in data
• Widgets and events add interactivity for data exploration
• Mastering these tools enables the creation of interactive dashboards and visual storytelling

---

### Exercise

• Plot a 3D surface of z = cos(sqrt(x² + y²)).
• Create a slider to change frequency of a sine wave in real-time.
• Animate a circle that rotates along time.
• Build a 3D scatter plot of 3 correlated variables.

---

#Python #Matplotlib #3DPlots #Animations #InteractiveVisuals #DataVisualization

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Topic: Python Matplotlib – Important 20 Interview Questions with Answers

---

### 1. What is Matplotlib in Python?

Answer:
Matplotlib is a comprehensive library for creating static, animated, and interactive visualizations in Python. It is highly customizable and works well with NumPy and pandas.

---

### 2. What is the difference between `plt.plot()` and `plt.scatter()`?

Answer:
• plt.plot() is used for line plots.
• plt.scatter() is used for creating scatter (dot) plots.

---

### 3. How do you add a title and axis labels to a plot?

Answer:

plt.title("My Plot")
plt.xlabel("X-axis")
plt.ylabel("Y-axis")

---

### 4. How can you create multiple subplots in one figure?

Answer:
Use plt.subplots() to create a grid layout of subplots.

fig, axs = plt.subplots(2, 2)

---

### 5. How do you save a plot to a file?

Answer:

plt.savefig("myplot.png", dpi=300)

---

### 6. What is the role of `plt.show()`?

Answer:
It displays the figure window containing the plot. Required for interactive sessions or scripts.

---

### 7. What is a histogram in Matplotlib?

Answer:
A histogram is used to visualize the frequency distribution of numeric data using plt.hist().

---

### 8. What does `plt.figure(figsize=(8,6))` do?

Answer:
It creates a new figure with a specified width and height (in inches).

---

### 9. How do you add a legend to your plot?

Answer:

plt.legend()

You must specify label='something' in your plot function.

---

### 10. What are some common `cmap` (color map) options?

Answer:
'viridis', 'plasma', 'hot', 'coolwarm', 'gray', 'jet', etc.

---

### 11. How do you create a bar chart?

Answer:

plt.bar(categories, values)

---

### 12. How can you rotate x-axis tick labels?

Answer:

plt.xticks(rotation=45)

---

### 13. How do you add a grid to the plot?

Answer:

plt.grid(True)

---

### 14. What is the difference between `imshow()` and `matshow()`?

Answer:
• imshow() is general-purpose for image data.
• matshow() is optimized for 2D matrices and auto-configures the axes.

---

### 15. How do you change the style of a plot globally?

Answer:

plt.style.use('ggplot')

---

### 16. How can you add annotations to specific data points?

Answer:

plt.annotate('label', xy=(x, y), xytext=(x+1, y+1), arrowprops=dict(arrowstyle='->'))

---

### 17. How do you create a pie chart in Matplotlib?

Answer:

plt.pie(data, labels=labels, autopct='%1.1f%%')

---

### 18. How do you plot a heatmap in Matplotlib?

Answer:

plt.imshow(matrix, cmap='hot')
plt.colorbar()

---

### 19. Can Matplotlib create 3D plots?

Answer:
Yes. Use:

from mpl_toolkits.mplot3d import Axes3D

Then:

fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')

---

### 20. How do you add error bars to your data?

Answer:

plt.errorbar(x, y, yerr=errors, fmt='o')

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### Exercise

Choose 5 of the above functions and implement a mini-dashboard with line, bar, and pie plots in one figure layout.

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#Python #Matplotlib #InterviewQuestions #DataVisualization #TechInterview

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