Cumulative histograms in Matplotlib - Mini Project: Build & Apply

Cumulative histograms

📖 Scenario: You are analyzing the daily sales numbers of a small store over a week. You want to understand how sales accumulate over the days.

🎯 Goal: Create a cumulative histogram using matplotlib to visualize the accumulation of sales over the week.

📋 What You'll Learn

Create a list called daily_sales with exact sales numbers for 7 days

Create a variable called bins to define histogram bins

Use plt.hist() with cumulative=True to create a cumulative histogram

Display the histogram with plt.show()

💡 Why This Matters

🌍 Real World

Cumulative histograms help businesses see how quantities add up over time or categories, like total sales or accumulated customers.

💼 Career

Data analysts and scientists use cumulative histograms to understand trends and distributions in data for better decision-making.

1

Create the daily sales data

Create a list called daily_sales with these exact values: 5, 8, 6, 10, 7, 9, 4 representing sales for 7 days.

Matplotlib

# Create the daily_sales list with the exact values
# Your code here

Hint

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

2

Define histogram bins

Create a variable called bins and set it to a list with these exact values: 0, 3, 6, 9, 12 to define the histogram bins.

Matplotlib

daily_sales = [5, 8, 6, 10, 7, 9, 4]
# Create the bins list with the exact values
# Your code here

Hint

Bins are the edges for grouping data in the histogram. Use a list with the exact numbers.

3

Create the cumulative histogram

Import matplotlib.pyplot as plt. Then use plt.hist() with daily_sales, bins, and cumulative=True to create a cumulative histogram.

Matplotlib

daily_sales = [5, 8, 6, 10, 7, 9, 4]
bins = [0, 3, 6, 9, 12]
# Import matplotlib.pyplot as plt
# Create cumulative histogram with plt.hist()
# Your code here

Hint

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

4

Display the histogram

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

Matplotlib

import matplotlib.pyplot as plt
daily_sales = [5, 8, 6, 10, 7, 9, 4]
bins = [0, 3, 6, 9, 12]
plt.hist(daily_sales, bins=bins, cumulative=True)
# Display the plot
# Your code here

Hint

Call plt.show() to open the plot window and see the histogram.

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