Multiple histograms overlay in Matplotlib - Practice Problems & Coding Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

Output of overlaying two histograms with transparency

What is the output of this code that overlays two histograms with alpha transparency?

Matplotlib

import matplotlib.pyplot as plt
import numpy as np

np.random.seed(0)
data1 = np.random.normal(0, 1, 1000)
data2 = np.random.normal(2, 1, 1000)

plt.hist(data1, bins=30, alpha=0.5, label='Data 1')
plt.hist(data2, bins=30, alpha=0.5, label='Data 2')
plt.legend()
plt.show()

A Two overlapping histograms with semi-transparent bars, one centered near 0 and the other near 2, both visible with legend labels.

B A single histogram combining both datasets into one, centered near 1 with no transparency or legend.

C Two histograms plotted side by side without overlap, each with full opacity and no transparency.

D An empty plot with no bars visible because alpha is set to 0.

💡 Hint

Look at the alpha parameter controlling transparency and how plt.hist overlays multiple calls.

The code plots two histograms on the same axes with alpha=0.5, so bars overlap with transparency. The first dataset centers near 0, the second near 2. The legend shows labels for both.

❓ data_output

intermediate

Number of bars in overlaid histograms

Given two datasets each with 1000 points, and histograms plotted with bins=20 overlaid, how many bars are visible in total?

Matplotlib

import numpy as np
import matplotlib.pyplot as plt

data1 = np.random.normal(0, 1, 1000)
data2 = np.random.normal(1, 1, 1000)

plt.hist(data1, bins=20, alpha=0.6)
plt.hist(data2, bins=20, alpha=0.6)
plt.show()

A 40 bars total, 20 bars for each histogram overlaid.

B 20 bars total, because the histograms overlap on the same bins.

C 10 bars total, because bins are shared and combined.

D No bars visible because alpha is less than 1.

💡 Hint

Each plt.hist call creates its own set of bars even if bins are the same.

Each histogram call creates 20 bars. Overlaying two histograms with bins=20 results in 40 bars total, 20 per dataset, drawn on top of each other.

🔧 Debug

advanced

Why does this overlaid histogram code show only one dataset?

This code intends to overlay two histograms but only shows one. What is the cause?

Matplotlib

import matplotlib.pyplot as plt
import numpy as np

data1 = np.random.normal(0, 1, 1000)
data2 = np.random.normal(3, 1, 1000)

plt.hist(data1, bins=25, alpha=0.7, label='Data 1')
plt.hist(data2, bins=25, alpha=0.7, label='Data 2')
plt.legend()
plt.show()

A The histograms are plotted correctly but the legend is missing so it looks like one dataset.

B The second histogram is not plotted because plt.hist overwrites the first call by default.

C The second histogram is plotted but fully covers the first because both have the same color and no transparency.

D The alpha value is too low, making the first histogram invisible.

💡 Hint

Check the default color and alpha values and how they affect visibility.

Both histograms use the default color (blue) and alpha=0.7, so the second fully covers the first. Transparency is not enough to see both distinctly.

❓ visualization

advanced

Effect of different bin sizes on overlaid histograms

What happens visually when overlaying two histograms with different bin sizes?

Matplotlib

import matplotlib.pyplot as plt
import numpy as np

np.random.seed(1)
data1 = np.random.normal(0, 1, 1000)
data2 = np.random.normal(1, 1, 1000)

plt.hist(data1, bins=15, alpha=0.5, label='Bins=15')
plt.hist(data2, bins=30, alpha=0.5, label='Bins=30')
plt.legend()
plt.show()

A Both histograms have bars of the same width because matplotlib normalizes bin sizes automatically.

B The histogram with 15 bins has wider bars, the one with 30 bins has narrower bars, both visible overlapping with transparency.

C Only the histogram with 30 bins is visible because it overwrites the other.

D The plot shows an error because bins must be the same for overlaying histograms.

💡 Hint

Think about how bin count affects bar width and how matplotlib draws multiple histograms.

Different bin counts produce bars of different widths. Overlaying them shows wider bars for 15 bins and narrower bars for 30 bins, both visible with alpha transparency.

🚀 Application

expert

Interpreting overlapping histograms for two groups

You have two groups of exam scores. Group A scores center around 70, Group B around 85. You overlay histograms with bins=20 and alpha=0.4. What can you infer from the plot?

Matplotlib

import matplotlib.pyplot as plt
import numpy as np

np.random.seed(42)
score_A = np.random.normal(70, 10, 500)
score_B = np.random.normal(85, 10, 500)

plt.hist(score_A, bins=20, alpha=0.4, label='Group A')
plt.hist(score_B, bins=20, alpha=0.4, label='Group B')
plt.legend()
plt.show()

A Both groups have identical score distributions because histograms overlap perfectly.

B The histograms cannot be compared because alpha=0.4 makes bars too transparent to see.

C Group A scored higher than Group B because its histogram bars are taller.

D Group B generally scored higher than Group A, but there is some overlap in score ranges visible in the histogram.

💡 Hint

Look at where the peaks of the histograms are and how much they overlap.

Group B's histogram centers around 85, higher than Group A's 70. The overlap shows some scores are similar, but overall Group B scored higher.

Practice

1. What is the main purpose of overlaying multiple histograms in a single plot using matplotlib?

easy

A. To sort data values in ascending order

B. To create a pie chart from histogram data

C. To calculate the mean of multiple datasets

D. To visually compare the distribution of different data groups in one plot

Solution

1. Step 1: Understand histogram purpose

   A histogram shows how data values are distributed across ranges.

2. Step 2: Purpose of overlaying

   Overlaying multiple histograms lets us see and compare distributions of different groups in one plot.

3. Final Answer:

   To visually compare the distribution of different data groups in one plot -> Option D

4. Quick Check:

   Overlay = Compare distributions [OK]

Hint: Overlay histograms to compare groups visually [OK]

Common Mistakes:

• Thinking overlay sorts data
• Confusing histogram with pie chart
• Assuming overlay calculates statistics

2. Which of the following matplotlib code snippets correctly overlays two histograms with transparency?

easy

A. plt.hist(data1); plt.hist(data2, alpha=2)

B. plt.hist(data1, alpha=0.5); plt.hist(data2, alpha=0.5)

C. plt.hist(data1, transparency=0.5); plt.hist(data2, transparency=0.5)

D. plt.hist(data1, alpha=1.5); plt.hist(data2, alpha=1.5)

Solution

1. Step 1: Check correct parameter for transparency

   In matplotlib, alpha controls transparency and must be between 0 and 1.

2. Step 2: Validate each option

   plt.hist(data1, alpha=0.5); plt.hist(data2, alpha=0.5) uses alpha=0.5 correctly for both histograms. Options B and D use invalid alpha values (>1). plt.hist(data1, transparency=0.5); plt.hist(data2, transparency=0.5) uses a wrong parameter name transparency.

3. Final Answer:

   plt.hist(data1, alpha=0.5); plt.hist(data2, alpha=0.5) -> Option B

4. Quick Check:

   Use alpha between 0 and 1 for transparency [OK]

Hint: Use alpha between 0 and 1 for transparency [OK]

Common Mistakes:

• Using alpha values greater than 1
• Using wrong parameter names like transparency
• Omitting alpha causing no overlay visibility

3. What will be the output of this code?

import matplotlib.pyplot as plt
import numpy as np
np.random.seed(0)
data1 = np.random.normal(0, 1, 100)
data2 = np.random.normal(2, 1, 100)
plt.hist(data1, bins=20, alpha=0.6, label='Group 1')
plt.hist(data2, bins=20, alpha=0.6, label='Group 2')
plt.legend()
plt.show()

medium

A. Two overlapping histograms with semi-transparent bars and a legend showing 'Group 1' and 'Group 2'

B. A single histogram combining data1 and data2 without transparency

C. An error because bins parameter is missing

D. Two histograms plotted side by side without overlap

Solution

1. Step 1: Analyze histogram parameters

   Both histograms use 20 bins and alpha=0.6 for transparency, so bars will overlap but remain visible.

2. Step 2: Check legend and plot behavior

   Labels are set and legend is called, so legend will show 'Group 1' and 'Group 2'. Histograms overlay, not side by side.

3. Final Answer:

   Two overlapping histograms with semi-transparent bars and a legend showing 'Group 1' and 'Group 2' -> Option A

4. Quick Check:

   Alpha + legend = overlapping histograms with labels [OK]

Hint: Alpha makes bars transparent; legend shows labels [OK]

Common Mistakes:

• Thinking histograms combine data automatically
• Expecting side-by-side bars without specifying
• Missing legend despite label parameter

4. Identify the error in this code that tries to overlay two histograms:

plt.hist(data1, bins=15, alpha=0.4, label='A')
plt.hist(data2, bins=15, alpha=0.4)
plt.legend()
plt.show()

medium

A. Alpha value 0.4 is invalid and causes runtime error

B. Bins parameter must be different for each histogram

C. Missing label for the second histogram causes legend to show only one label

D. plt.legend() must be called before plotting histograms

Solution

1. Step 1: Check labels for legend

   The first histogram has label 'A', but the second histogram has no label, so legend will show only one entry.

2. Step 2: Validate other parameters

   Alpha=0.4 is valid. Bins can be same for overlay. Legend can be called after plotting.

3. Final Answer:

   Missing label for the second histogram causes legend to show only one label -> Option C

4. Quick Check:

   All histograms need labels for legend entries [OK]

Hint: Add labels to all histograms for complete legend [OK]

Common Mistakes:

• Assuming alpha=0.4 is invalid
• Thinking bins must differ for overlay
• Calling legend before plotting causes error

5. You have three datasets with very different sizes: data1 (1000 points), data2 (100 points), and data3 (10 points). You want to overlay their histograms fairly so that the smaller datasets are visible and comparable. Which approach is best?

hard

A. Use density=True in plt.hist for all datasets and set alpha=0.5 with labels

B. Plot histograms without transparency and use default counts

C. Use different bin sizes for each dataset without normalization

D. Plot only the largest dataset to avoid clutter

Solution

1. Step 1: Understand size difference impact

   Datasets with different sizes produce histograms with very different counts, making small datasets hard to see.

2. Step 2: Use density normalization and transparency

   Setting density=True normalizes histograms to show probability density, making them comparable regardless of size. Using alpha=0.5 allows overlapping visibility. Adding labels helps identify each.

3. Final Answer:

   Use density=True in plt.hist for all datasets and set alpha=0.5 with labels -> Option A

4. Quick Check:

   Normalize with density=True + alpha for visibility [OK]

Hint: Normalize histograms with density=True for fair comparison [OK]

Common Mistakes:

• Not normalizing causes small datasets to be invisible
• Using opaque bars hides overlaps
• Changing bins without normalization confuses comparison