Multiple histograms overlay in Matplotlib - Step-by-Step Execution

Concept Flow - Multiple histograms overlay

Prepare data sets

↓

Call plt.hist() for each data set with alpha

↓

Histograms drawn on same plot

↓

Add labels, legend, title

↓

Show combined histogram plot

We prepare multiple data sets, then draw their histograms on the same plot with transparency to see overlaps.

Execution Sample

Matplotlib

import matplotlib.pyplot as plt
import numpy as np

# Two data sets
data1 = np.random.normal(0, 1, 1000)
data2 = np.random.normal(2, 1.5, 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()

This code draws two histograms on the same plot with some transparency so we can see where they overlap.

Execution Table

Step	Action	Data Used	Bins	Alpha	Plot State	Output
1	Generate data1	Normal(0,1), 1000 points	-	-	No plot yet	data1 array created
2	Generate data2	Normal(2,1.5), 1000 points	-	-	No plot yet	data2 array created
3	Plot histogram for data1	data1	30	0.5	Plot with data1 histogram	Histogram bars for data1 shown with 50% transparency
4	Plot histogram for data2	data2	30	0.5	Plot with data1 and data2 histograms	Histogram bars for data2 shown overlapping data1 with 50% transparency
5	Add legend	-	-	-	Plot with legend	Legend shows 'Data 1' and 'Data 2' labels
6	Show plot	-	-	-	Plot displayed	Combined histogram plot visible with overlays

💡 All steps complete, plot shown with both histograms overlayed.

Variable Tracker

Variable	Start	After Step 1	After Step 2	After Step 3	After Step 4	Final
data1	None	Array of 1000 values ~ N(0,1)	Array unchanged	Array unchanged	Array unchanged	Array unchanged
data2	None	None	Array of 1000 values ~ N(2,1.5)	Array unchanged	Array unchanged	Array unchanged
plot_state	Empty	Empty	Empty	Histogram of data1 drawn	Histograms of data1 and data2 drawn	Plot with legend and shown

Key Moments - 3 Insights

Why do we use alpha=0.5 when plotting multiple histograms?

Alpha sets transparency. Using 0.5 lets us see overlapping bars clearly, as shown in execution_table steps 3 and 4.

What happens if we don't call plt.legend() after plotting?

Without plt.legend(), the plot won't show labels for each histogram, making it hard to tell which bars belong to which data set (see step 5).

Why do both histograms use the same number of bins?

Using the same bins (30 here) aligns the bars for easy comparison, as seen in steps 3 and 4.

Visual Quiz - 3 Questions

Look at the execution_table at step 4. What does the plot state show after plotting data2?

A Plot with data1 and data2 histograms overlayed

B Plot with only data2 histogram

C Empty plot with no histograms

D Plot with legend only

💡 Hint

Check the 'Plot State' column at step 4 in execution_table.

At which step is the legend added to the plot?

A Step 3

B Step 5

C Step 4

D Step 6

💡 Hint

Look for the action 'Add legend' in execution_table.

If we remove alpha=0.5 from both plt.hist calls, what will happen to the plot?

A Histograms will be transparent and easy to compare

B Plot will show no histograms

C Histograms will be fully opaque and overlapping bars may hide each other

D Plot will show only one histogram

💡 Hint

Refer to key_moments about the role of alpha transparency.

Concept Snapshot

Multiple histograms overlay:
- Use plt.hist() multiple times on same plot
- Use same bins for alignment
- Use alpha (0-1) for transparency
- Add labels and plt.legend() for clarity
- Call plt.show() to display combined plot

Full Transcript

This visual execution shows how to overlay multiple histograms using matplotlib. First, two data sets are created with different normal distributions. Then, plt.hist() is called twice with the same number of bins and alpha=0.5 for transparency. This allows both histograms to appear on the same plot, showing overlaps clearly. A legend is added to label each histogram. Finally, plt.show() displays the combined plot. Key points include using alpha for transparency and adding a legend for clarity.

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