Normalized histograms in Matplotlib - Interactive Code Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to plot a normalized histogram using matplotlib.

Matplotlib

import matplotlib.pyplot as plt

data = [1, 2, 2, 3, 3, 3, 4, 4, 4, 4]
plt.hist(data, density=[1])
plt.show()

Drag options to blanks, or click blank then click option'

ANone

BFalse

CTrue

D0

Attempts:

3 left

💡 Hint

Common Mistakes

Using density=False will plot counts instead of probabilities.

Passing None or 0 does not normalize the histogram.

Setting density=True normalizes the histogram so the area sums to 1.

2fill in blank

medium

Complete the code to plot a normalized histogram with 5 bins.

Matplotlib

import matplotlib.pyplot as plt

values = [5, 7, 7, 8, 9, 10, 10, 10, 11]
plt.hist(values, bins=[1], density=True)
plt.show()

Drag options to blanks, or click blank then click option'

A3

B10

C7

D5

Attempts:

3 left

💡 Hint

Common Mistakes

Using too few bins can hide data details.

Using too many bins can make the histogram noisy.

Setting bins=5 divides the data into 5 equal-width bins.

3fill in blank

hard

Fix the error in the code to correctly plot a normalized histogram.

Matplotlib

import matplotlib.pyplot as plt

scores = [60, 70, 70, 80, 90, 90, 90, 100]
plt.hist(scores, bins=4, [1]=True)
plt.show()

Drag options to blanks, or click blank then click option'

Anormalize

Bdensity

Cnormed

Dprobability

Attempts:

3 left

💡 Hint

Common Mistakes

Using deprecated or incorrect parameter names like 'normed'.

Using 'normalize' or 'probability' which are not valid parameters.

The correct parameter to normalize histograms in matplotlib is density.

4fill in blank

hard

Fill both blanks to create a normalized histogram with 6 bins and blue color.

Matplotlib

import matplotlib.pyplot as plt

ages = [22, 25, 25, 30, 35, 35, 40, 45, 50]
plt.hist(ages, bins=[1], density=[2], color='blue')
plt.show()

Drag options to blanks, or click blank then click option'

A6

BTrue

CFalse

D5

Attempts:

3 left

💡 Hint

Common Mistakes

Using density=False will not normalize the histogram.

Setting bins to 5 instead of 6 changes the bin count.

Use bins=6 to set six bins and density=True to normalize the histogram.

5fill in blank

hard

Fill all three blanks to create a normalized histogram with red color, 4 bins, and alpha transparency 0.7.

Matplotlib

import matplotlib.pyplot as plt

weights = [55, 60, 65, 70, 75, 80, 85, 90]
plt.hist(weights, bins=[1], density=[2], color=[3], alpha=0.7)
plt.show()

Drag options to blanks, or click blank then click option'

ATrue

B4

C'red'

D'blue'

Attempts:

3 left

💡 Hint

Common Mistakes

Mixing up color strings or using wrong bin counts.

Setting density to False will not normalize the histogram.

Set bins=4 for four bins, density=True to normalize, and color='red' for red bars.

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