Cumulative histograms in Matplotlib - Interactive Code Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to plot a cumulative histogram using matplotlib.

Matplotlib

import matplotlib.pyplot as plt
import numpy as np

data = np.random.randn(1000)
plt.hist(data, bins=30, cumulative=[1])
plt.show()

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

ATrue

BFalse

CNone

D0

Attempts:

3 left

💡 Hint

Common Mistakes

Using cumulative=False will plot a normal histogram.

Passing None or 0 will not create a cumulative histogram.

Setting cumulative=True makes the histogram cumulative.

2fill in blank

medium

Complete the code to add labels and a title to the cumulative histogram.

Matplotlib

import matplotlib.pyplot as plt
import numpy as np

data = np.random.randn(1000)
plt.hist(data, bins=20, cumulative=True)
plt.xlabel([1])
plt.ylabel('Frequency')
plt.title('Cumulative Histogram')
plt.show()

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

A'Values'

B'Bins'

C'Data values'

D'X-axis'

Attempts:

3 left

💡 Hint

Common Mistakes

Using 'Bins' as xlabel is less clear than 'Values'.

Leaving xlabel empty makes the plot less understandable.

The x-axis label should describe the data values shown in the histogram.

3fill in blank

hard

Fix the error in the code to correctly plot a cumulative histogram with density normalization.

Matplotlib

import matplotlib.pyplot as plt
import numpy as np

data = np.random.randn(1000)
plt.hist(data, bins=25, cumulative=[1], density=True)
plt.show()

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

A0

BTrue

CNone

DFalse

Attempts:

3 left

💡 Hint

Common Mistakes

Setting cumulative=False will plot a normal histogram.

Using None or 0 for cumulative causes the histogram to be non-cumulative.

To plot a cumulative histogram with density normalization, set cumulative=True.

4fill in blank

hard

Fill both blanks to create a cumulative histogram with 40 bins and a blue color.

Matplotlib

import matplotlib.pyplot as plt
import numpy as np

data = np.random.randn(1000)
plt.hist(data, bins=[1], cumulative=True, color=[2])
plt.show()

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

A40

B'red'

C'blue'

D30

Attempts:

3 left

💡 Hint

Common Mistakes

Using a string for bins causes an error.

Using a color name without quotes causes an error.

Use 40 bins and set color to 'blue' for the histogram.

5fill in blank

hard

Fill all three blanks to create a cumulative histogram with green color, 50 bins, and alpha transparency 0.5.

Matplotlib

import matplotlib.pyplot as plt
import numpy as np

data = np.random.randn(1000)
plt.hist(data, bins=[1], cumulative=True, color=[2], alpha=[3])
plt.show()

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

A40

B50

C'green'

D0.5

Attempts:

3 left

💡 Hint

Common Mistakes

Using alpha as a string causes an error.

Using color without quotes causes an error.

Set bins to 50, color to 'green', and alpha to 0.5 for transparency.

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