Cumulative histograms in Matplotlib - Practice Problems & Coding Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

Output of cumulative histogram with uniform data

What is the output array of counts for the cumulative histogram of 10 numbers from 1 to 10 with 5 bins?

Matplotlib

import numpy as np
import matplotlib.pyplot as plt

data = np.arange(1, 11)
counts, bins, patches = plt.hist(data, bins=5, cumulative=True)
plt.close()
print(counts)

A [2. 3. 5. 7. 10.]

B [1. 2. 3. 4. 5.]

C [0. 2. 4. 6. 8.]

D [2. 4. 6. 8. 10.]

💡 Hint

Think about how cumulative counts add up across bins.

The data has 10 values evenly spaced from 1 to 10. With 5 bins, each bin covers 2 numbers. The cumulative counts add up the number of data points up to each bin edge, resulting in [2, 4, 6, 8, 10].

❓ data_output

intermediate

Number of bins in cumulative histogram

If you create a cumulative histogram with 7 bins from data of 50 random values, how many count values will the output array have?

Matplotlib

import numpy as np
import matplotlib.pyplot as plt

data = np.random.randn(50)
counts, bins, patches = plt.hist(data, bins=7, cumulative=True)
plt.close()
print(len(counts))

A 50

B 6

C 7

D 8

💡 Hint

The counts array length matches the number of bins.

The counts array length equals the number of bins specified, which is 7.

❓ visualization

advanced

Identify the cumulative histogram plot

Which plot shows a cumulative histogram of data sampled from a normal distribution?

Matplotlib

import numpy as np
import matplotlib.pyplot as plt

data = np.random.normal(0, 1, 1000)
plt.figure(figsize=(8,4))
plt.subplot(1,2,1)
plt.hist(data, bins=30)
plt.title('Regular Histogram')
plt.subplot(1,2,2)
plt.hist(data, bins=30, cumulative=True)
plt.title('Cumulative Histogram')
plt.tight_layout()
plt.show()

A The right plot with bars increasing and never decreasing

B Neither plot is a histogram

C Both plots show cumulative histograms

D The left plot with bars showing frequency counts

💡 Hint

Cumulative histograms always increase or stay the same as bins increase.

The right plot uses cumulative=True, so the bars accumulate counts and never decrease, showing a cumulative histogram.

🧠 Conceptual

advanced

Effect of cumulative=True on histogram counts

What happens to the counts array when you set cumulative=True in plt.hist compared to cumulative=False?

A Counts become negative for bins with no data

B Counts show total data points up to each bin edge, increasing or staying the same

C Counts show only the data points in each bin, independent of previous bins

D Counts are normalized to sum to 1

💡 Hint

Cumulative means adding up counts as you move through bins.

With cumulative=True, counts accumulate data points from all previous bins, so counts never decrease.

🔧 Debug

expert

Identify the error in cumulative histogram code

What error does this code raise? import matplotlib.pyplot as plt plt.hist([1,2,3,4,5], bins=3, cumulative='yes')

Matplotlib

import matplotlib.pyplot as plt

plt.hist([1,2,3,4,5], bins=3, cumulative='yes')

A TypeError: cumulative must be a boolean, not str

B ValueError: bins must be an integer or sequence

C SyntaxError: invalid syntax

D No error, runs successfully

💡 Hint

Check the type expected for the cumulative parameter.

The cumulative parameter expects a boolean True or False, not a string. Passing 'yes' causes a TypeError.

Practice

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

easy

A. It shows the total counts accumulated up to each bin.

B. It changes the histogram to a bar chart.

C. It normalizes the histogram to show probabilities.

D. It colors the bars based on their height.

Solution

1. Step 1: Understand the cumulative parameter

   Setting cumulative=True in plt.hist() changes the histogram to show accumulated counts.

2. Step 2: Effect on histogram output

   Instead of showing counts per bin, it shows the sum of counts up to that bin, making the histogram cumulative.

3. Final Answer:

   It shows the total counts accumulated up to each bin. -> Option A

4. Quick Check:

   cumulative=True means accumulation [OK]

Hint: Remember cumulative=True sums counts up to each bin [OK]

Common Mistakes:

• Thinking it normalizes the histogram
• Confusing cumulative with coloring
• Assuming it changes chart type to bar chart

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

easy

A. plt.hist(data, cumulative=True)

B. plt.hist(data, cumulative=0)

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

D. plt.hist(data, cumulative)

Solution

1. Step 1: Check correct parameter name and usage

   The correct parameter to make a histogram cumulative is cumulative=True.

2. Step 2: Validate syntax correctness

   plt.hist(data, cumulative=True) uses the exact correct syntax. plt.hist(data, cumulative=0) uses 0 instead of True (no cumulative effect). plt.hist(data, cumulate=True) misspells the parameter. plt.hist(data, cumulative) is invalid syntax.

3. Final Answer:

   plt.hist(data, cumulative=True) -> Option A

4. Quick Check:

   Use cumulative=True exactly [OK]

Hint: Use cumulative=True exactly for cumulative histograms [OK]

Common Mistakes:

• Misspelling 'cumulative' parameter
• Using cumulative without assignment
• Using cumulative=0 (disables cumulative)

3. What will be the output counts of the cumulative histogram bins for data = [1, 2, 2, 3, 4] with bins [1, 2, 3, 4, 5] using plt.hist(data, bins=[1,2,3,4,5], cumulative=True)?

medium

A. [0, 1, 3, 5]

B. [1, 3, 4, 5]

C. [1, 1, 2, 3]

D. [1, 2, 3, 4]

Solution

1. Step 1: Count data points in each bin

   Bins: [1-2), [2-3), [3-4), [4-5). Counts per bin: 1 in first, 2 in second, 1 in third, 1 in fourth.

2. Step 2: Calculate cumulative counts

   Cumulative sums: 1, 1+2=3, 3+1=4, 4+1=5.

3. Final Answer:

   [1, 3, 4, 5] -> Option B

4. Quick Check:

   Cumulative sums of counts = [1,3,4,5] [OK]

Hint: Add counts bin by bin for cumulative totals [OK]

Common Mistakes:

• Counting bins inclusively instead of half-open
• Not summing counts cumulatively
• Miscounting data points per bin

4. The code below is intended to plot a cumulative histogram but does not produce the expected cumulative effect. What is the error?

import matplotlib.pyplot as plt
data = [1,2,2,3,4]
plt.hist(data, bins=4, cumulative=False)
plt.show()

medium

A. The bins parameter must be a list, not an integer.

B. plt.show() is missing and must be added.

C. The parameter cumulative should be set to True, not False.

D. Data list must be sorted before plotting.

Solution

1. Step 1: Identify the cumulative parameter usage

   The code sets cumulative=False, so the histogram is not cumulative.

2. Step 2: Correct the parameter to get cumulative histogram

   Changing cumulative=False to cumulative=True will produce the cumulative histogram as intended.

3. Final Answer:

   The parameter cumulative should be set to True, not False. -> Option C

4. Quick Check:

   cumulative=True needed for cumulative histogram [OK]

Hint: Set cumulative=True to enable cumulative histogram [OK]

Common Mistakes:

• Leaving cumulative=False by mistake
• Thinking bins must be a list always
• Believing data must be sorted
• Forgetting plt.show() (though present here)

5. You have two datasets: data1 = [1,2,3,4,5] and data2 = [2,3,4,5,6]. You want to plot their cumulative histograms on the same plot to compare their distributions. Which code snippet correctly does this?

hard

A. plt.hist([data1, data2], bins=6, cumulative=False, label=['Data1', 'Data2']); plt.legend(); plt.show()

B. plt.hist(data1 + data2, bins=6, cumulative=True); plt.show()

C. plt.hist(data1, bins=6); plt.hist(data2, bins=6); plt.show()

D. plt.hist([data1, data2], bins=6, cumulative=True, label=['Data1', 'Data2'], histtype='step'); plt.legend(); plt.show()

Solution

1. Step 1: Understand plotting multiple cumulative histograms

   To compare cumulative histograms, pass both datasets as a list, set cumulative=True, and use histtype='step' for clarity.

2. Step 2: Check options for correct parameters

   plt.hist([data1, data2], bins=6, cumulative=True, label=['Data1', 'Data2'], histtype='step'); plt.legend(); plt.show() correctly uses plt.hist([data1, data2], bins=6, cumulative=True, label=['Data1', 'Data2'], histtype='step') with legend and show. plt.hist(data1 + data2, bins=6, cumulative=True); plt.show() incorrectly combines the datasets into one histogram. plt.hist(data1, bins=6); plt.hist(data2, bins=6); plt.show() is not cumulative. plt.hist([data1, data2], bins=6, cumulative=False, label=['Data1', 'Data2']); plt.legend(); plt.show() is not cumulative.

3. Final Answer:

   plt.hist([data1, data2], bins=6, cumulative=True, label=['Data1', 'Data2'], histtype='step'); plt.legend(); plt.show() -> Option D

4. Quick Check:

   Multiple datasets + cumulative=True + histtype='step' = plt.hist([data1, data2], bins=6, cumulative=True, label=['Data1', 'Data2'], histtype='step'); plt.legend(); plt.show() [OK]

Hint: Use list of datasets and cumulative=True with histtype='step' [OK]

Common Mistakes:

• Combining datasets into a single histogram
• Forgetting cumulative=True
• Not using histtype='step' for clear lines
• Using cumulative=False by mistake