Normalized histograms in Matplotlib - Mini Project: Build & Apply

Normalized histograms

📖 Scenario: You are analyzing the heights of a group of people. You want to see how the heights are spread out using a histogram. But instead of just counting how many people fall into each height range, you want to see the relative frequency so you can compare it easily with other groups.

🎯 Goal: Create a normalized histogram of the heights data using matplotlib. This means the histogram bars will show proportions instead of counts.

📋 What You'll Learn

Create a list called heights with exact values

Create a variable called bins to set the number of bins

Use matplotlib's hist() function with density=True to create a normalized histogram

Display the histogram with plt.show()

💡 Why This Matters

🌍 Real World

Normalized histograms help compare data distributions fairly, especially when sample sizes differ. For example, comparing heights of people from different cities.

💼 Career

Data scientists use normalized histograms to visualize and compare data distributions clearly, which helps in making data-driven decisions.

1

Create the heights data

Create a list called heights with these exact values: 160, 165, 170, 160, 175, 180, 170, 165, 160, 175.

Matplotlib

# Create the list heights with the given values
# Your code here

Hint

Use square brackets to create a list and separate numbers with commas.

2

Set the number of bins

Create a variable called bins and set it to 5 to divide the heights into 5 groups.

Matplotlib

heights = [160, 165, 170, 160, 175, 180, 170, 165, 160, 175]
# Create the variable bins and set it to 5
# Your code here

Hint

Just assign the number 5 to the variable bins.

3

Create the normalized histogram

Import matplotlib.pyplot as plt. Then use plt.hist() with the heights list and bins variable. Set density=True to normalize the histogram.

Matplotlib

heights = [160, 165, 170, 160, 175, 180, 170, 165, 160, 175]
bins = 5
# Import matplotlib.pyplot as plt
# Create a normalized histogram using plt.hist with density=True
# Your code here

Hint

Use import matplotlib.pyplot as plt and call plt.hist() with the right arguments.

4

Display the histogram

Use plt.show() to display the normalized histogram plot.

Matplotlib

import matplotlib.pyplot as plt

heights = [160, 165, 170, 160, 175, 180, 170, 165, 160, 175]
bins = 5

plt.hist(heights, bins=bins, density=True)
# Display the plot
# Your code here

Hint

Call plt.show() to see the histogram window.

Practice

1. What does setting density=True in plt.hist() do to the histogram?

easy

A. It changes the histogram bars to a different color.

B. It sorts the data before plotting the histogram.

C. It normalizes the histogram so the area sums to 1, showing probability density.

D. It plots the histogram with logarithmic scale on the y-axis.

Solution

1. Step 1: Understand the role of density=True

   Setting density=True scales the histogram so the total area under the bars equals 1.

2. Step 2: Interpret the effect on histogram

   This scaling means the histogram shows probability density instead of raw counts, useful for comparing distributions.

3. Final Answer:

   It normalizes the histogram so the area sums to 1, showing probability density. -> Option C

4. Quick Check:

   Normalized histogram = density=True [OK]

Hint: Remember: density=True makes area = 1, not counts [OK]

Common Mistakes:

• Thinking density=True changes colors
• Assuming density=True sorts data
• Confusing density=True with log scale

2. Which of the following is the correct syntax to plot a normalized histogram of data array data using matplotlib?

easy

A. plt.hist(data, scale='density')

B. plt.hist(data, density=True)

C. plt.hist(data, norm=True)

D. plt.hist(data, normalize=True)

Solution

1. Step 1: Recall matplotlib histogram parameters

   The correct parameter to normalize histogram counts is density=True.

2. Step 2: Check each option

   The other options use incorrect or nonexistent parameters for normalization.

3. Final Answer:

   plt.hist(data, density=True) -> Option B

4. Quick Check:

   Use density=True for normalized histogram [OK]

Hint: Use density=True exactly, no shortcuts [OK]

Common Mistakes:

• Using normalize=True which is invalid
• Trying norm=True instead of density=True
• Passing scale='density' which is not a parameter

3. What will be the output of this code snippet?

import matplotlib.pyplot as plt
import numpy as np
np.random.seed(0)
data = np.random.randint(1, 5, size=100)
counts, bins, patches = plt.hist(data, bins=4, density=True)
print(counts.round(2))

medium

A. [0.27 0.25 0.23 0.25]

B. [0.25 0.25 0.25 0.25]

C. [25 25 25 25]

D. [0.20 0.30 0.25 0.25]

Solution

1. Step 1: Understand data and bins

   Data has 100 integers between 1 and 4, bins=4 means bins cover 1-2, 2-3, 3-4, 4-5.

2. Step 2: Calculate normalized counts

   Using density=True, counts represent probability density, roughly proportional to frequency divided by bin width. The printed counts are close to [0.27, 0.25, 0.23, 0.25].

3. Final Answer:

   [0.27 0.25 0.23 0.25] -> Option A

4. Quick Check:

   Normalized counts sum to ~1 area [OK]

Hint: density=True scales counts to sum area 1 [OK]

Common Mistakes:

• Expecting raw counts instead of densities
• Confusing counts with percentages
• Ignoring bin width effect on density

4. Identify the error in this code that tries to plot a normalized histogram:

import matplotlib.pyplot as plt
data = [1, 2, 2, 3, 3, 3]
plt.hist(data, norm=True)
plt.show()

medium

A. plt.show() is missing and needed to display the plot.

B. The data list must be converted to a numpy array first.

C. Bins parameter is missing, causing an error.

D. The parameter 'norm' is invalid; should be 'density'.

Solution

1. Step 1: Check parameter names in plt.hist()

   The correct parameter to normalize histogram is density=True, not norm=True.

2. Step 2: Verify other parts

   Data can be a list, plt.show() is present, and bins are optional. So no error from those.

3. Final Answer:

   The parameter 'norm' is invalid; should be 'density'. -> Option D

4. Quick Check:

   Use density=True, not norm=True [OK]

Hint: Use density=True, not norm=True [OK]

Common Mistakes:

• Using norm=True instead of density=True
• Thinking data must be numpy array
• Forgetting plt.show() (though present here)
• Assuming bins are mandatory

5. You have two datasets with different sizes: data1 has 1000 points, data2 has 200 points. You want to compare their distributions fairly using histograms. Which approach is best?

hard

A. Plot histograms with density=True for both datasets.

B. Plot histograms with default counts for both datasets.

C. Plot histograms with different bin sizes for each dataset.

D. Plot histograms using cumulative counts.

Solution

1. Step 1: Understand the problem of different sizes

   Raw counts histograms will show higher bars for the larger dataset, making comparison unfair.

2. Step 2: Use normalized histograms

   Setting density=True scales histograms to probability densities, allowing fair comparison regardless of sample size.

3. Final Answer:

   Plot histograms with density=True for both datasets. -> Option A

4. Quick Check:

   Normalize histograms to compare different sizes [OK]

Hint: Normalize histograms to compare different sample sizes [OK]

Common Mistakes:

• Comparing raw counts directly
• Using different bin sizes causing bias
• Using cumulative counts which show totals, not densities