Expanding window operations in Pandas - Practice Problems & Coding Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

Output of expanding sum with min_periods

What is the output of the following code snippet using pandas expanding sum with min_periods=2?

Pandas

import pandas as pd
s = pd.Series([1, 2, 3, 4, 5])
result = s.expanding(min_periods=2).sum()
print(result.tolist())

A [nan, nan, 6.0, 10.0, 15.0]

B [1.0, 3.0, 6.0, 10.0, 15.0]

C [1, 3, 6, 10, 15]

D [nan, 3.0, 6.0, 10.0, 15.0]

💡 Hint

Remember that min_periods=2 means the expanding window will return NaN until at least 2 values are included.

The expanding sum with min_periods=2 returns NaN for the first element because there is only one value. From the second element onward, it sums all values up to that point.

❓ data_output

intermediate

Length of expanding window result

Given a pandas Series of length 7, what is the length of the Series returned by expanding().mean()?

Pandas

import pandas as pd
s = pd.Series(range(7))
result = s.expanding().mean()
print(len(result))

A 7

B 6

C 8

D 0

💡 Hint

The expanding window operation returns a result for each original element.

The expanding mean returns a Series of the same length as the original Series because it computes the mean for each expanding window ending at each element.

🔧 Debug

advanced

Identify the error in expanding window code

What error does the following code raise when executed?

Pandas

import pandas as pd
s = pd.Series([1, 2, 3])
result = s.expanding(min_periods=0).sum()
print(result)

A AttributeError: 'Series' object has no attribute 'expanding'

B ValueError: min_periods must be >= 1

C No error, prints [1, 3, 6]

D TypeError: unsupported operand type(s) for +: 'int' and 'NoneType'

💡 Hint

Check the allowed values for the min_periods parameter in expanding.

The min_periods parameter must be at least 1. Setting it to 0 raises a ValueError.

❓ visualization

advanced

Plotting expanding mean of a time series

Which option produces a line plot showing the original data and its expanding mean on the same graph?

Pandas

import pandas as pd
import matplotlib.pyplot as plt
s = pd.Series([2, 4, 6, 8, 10])
exp_mean = s.expanding().mean()
plt.figure()
plt.plot(s, label='Original')
plt.plot(exp_mean, label='Expanding Mean')
plt.legend()
plt.show()

A The plot shows two lines but both are flat at zero.

B The plot shows only one line identical to the original data.

C The plot shows two lines: the original increasing values and a smoother line starting at the first value and gradually increasing.

D The plot shows an error because matplotlib is not imported.

💡 Hint

The expanding mean smooths the data by averaging all values up to each point.

The expanding mean line starts at the first value and gradually approaches the original data values, showing a smoothing effect.

🚀 Application

expert

Using expanding window to detect trend changes

You have daily sales data in a pandas Series. You want to detect when the sales trend changes by comparing the expanding mean to the current value. Which code snippet correctly creates a boolean Series indicating if the current value is above the expanding mean?

A sales > sales.expanding().mean()

B sales.expanding().mean() > sales

C sales > sales.rolling(window=3).mean()

D sales.expanding(min_periods=0).mean() > sales

💡 Hint

Expanding mean includes all data up to current point; compare current value to it.

Option A compares the current sales value to the expanding mean correctly, producing a boolean Series indicating if sales are above the trend.

Practice

1. What does an expanding window operation in pandas do?

easy

A. Sorts data in ascending order

B. Calculates values only for a fixed-size sliding window

C. Filters data based on a condition

D. Calculates cumulative values including all previous data points

Solution

1. Step 1: Understand expanding window concept

   Expanding window operations include all data points from the start up to the current point.

2. Step 2: Compare with other window types

   Unlike rolling windows, expanding windows grow with each step, accumulating more data.

3. Final Answer:

   Calculates cumulative values including all previous data points -> Option D

4. Quick Check:

   Expanding window = cumulative calculation [OK]

Hint: Expanding means cumulative from start to current [OK]

Common Mistakes:

• Confusing expanding with rolling window
• Thinking it filters data
• Assuming it sorts data

2. Which of the following is the correct syntax to create an expanding window object on a pandas Series s?

easy

A. s.window()

B. s.expanding()

C. s.cumulative()

D. s.rolling()

Solution

1. Step 1: Recall pandas expanding syntax

   The method to create an expanding window object is expanding() called on a Series or DataFrame.

2. Step 2: Eliminate incorrect options

   rolling() is for rolling windows, cumulative() and window() do not exist as methods.

3. Final Answer:

   s.expanding() -> Option B

4. Quick Check:

   Use .expanding() for expanding windows [OK]

Hint: Use .expanding() method on Series/DataFrame [OK]

Common Mistakes:

• Using .rolling() instead of .expanding()
• Trying non-existent methods like .cumulative()
• Confusing window types

3. Given the pandas Series s = pd.Series([2, 4, 6, 8]), what is the output of s.expanding(min_periods=2).mean()?

medium

A. [NaN, 3.0, 4.0, 5.0]

B. [2.0, 3.0, 4.0, 5.0]

C. [NaN, 4.0, 6.0, 8.0]

D. [2.0, 4.0, 6.0, 8.0]

Solution

1. Step 1: Understand min_periods effect

   With min_periods=2, results start from the second element; first is NaN.

2. Step 2: Calculate expanding mean values

   Means are: index 1: (2+4)/2=3.0, index 2: (2+4+6)/3=4.0, index 3: (2+4+6+8)/4=5.0.

3. Final Answer:

   [NaN, 3.0, 4.0, 5.0] -> Option A

4. Quick Check:

   Expanding mean with min_periods=2 starts NaN then cumulative means [OK]

Hint: min_periods controls when output starts (NaN before) [OK]

Common Mistakes:

• Ignoring min_periods and showing first value
• Calculating rolling mean instead of expanding mean
• Miscomputing cumulative averages

4. What is wrong with this code snippet?

import pandas as pd
s = pd.Series([1, 2, 3])
result = s.expanding(min_periods=-1).sum()

medium

A. sum() cannot be used after expanding()

B. expanding() method does not exist for Series

C. min_periods cannot be negative; it must be >= 0

D. The Series must be converted to DataFrame first

Solution

1. Step 1: Check min_periods parameter rules

   min_periods must be >= 0; negative is invalid and causes an error.

2. Step 2: Verify method usage

   expanding() exists for Series, and sum() is valid after expanding().

3. Final Answer:

   min_periods cannot be negative; it must be >= 0 -> Option C

4. Quick Check:

   min_periods ≥ 0 required [OK]

Hint: min_periods must be >= 0, never negative [OK]

Common Mistakes:

• Setting min_periods to a negative value causing errors
• Thinking expanding() is unavailable for Series
• Misusing sum() after expanding()

5. You have daily sales data in a pandas DataFrame df with a column 'sales'. You want to calculate a running average of sales but only start showing results after at least 3 days of data. Which code correctly achieves this using expanding window operations?

hard

A. df['sales'].expanding(min_periods=3).mean()

B. df['sales'].rolling(window=3).mean()

C. df['sales'].expanding(min_periods=1).mean()

D. df['sales'].cumsum() / 3

Solution

1. Step 1: Understand requirement for running average with minimum data

   Expanding with min_periods=3 starts calculating mean only after 3 data points.

2. Step 2: Evaluate options

   df['sales'].expanding(min_periods=3).mean() uses expanding with min_periods=3 correctly. df['sales'].rolling(window=3).mean() uses rolling window, which is different. df['sales'].expanding(min_periods=1).mean() starts from 1 data point, not 3. df['sales'].cumsum() / 3 divides cumulative sum by 3 always, which is incorrect.

3. Final Answer:

   df['sales'].expanding(min_periods=3).mean() -> Option A

4. Quick Check:

   Expanding with min_periods=3 for running average [OK]

Hint: Use expanding(min_periods=3) for running average after 3 days [OK]

Common Mistakes:

• Using rolling instead of expanding
• Setting min_periods too low
• Dividing cumulative sum by fixed number