Window functions (expanding, ewm) in Data Analysis Python - Practice Problems & Coding Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

Output of expanding mean calculation

What is the output of the following code snippet that uses the expanding window function to calculate the mean?

Data Analysis Python

import pandas as pd
s = pd.Series([2, 4, 6, 8])
result = s.expanding().mean()
print(result.tolist())

A [2, 4, 6, 8]

B [2.0, 3.0, 4.0, 5.0]

C [2.0, 4.0, 6.0, 8.0]

D [2.0, 3.0, 5.0, 7.0]

💡 Hint

Think about how the expanding mean includes all values from the start up to the current position.

The expanding mean at each position is the average of all values from the first element up to that position. So for the series [2,4,6,8], the means are: 2, (2+4)/2=3, (2+4+6)/3=4, (2+4+6+8)/4=5.

❓ data_output

intermediate

Result of exponential weighted mean with alpha=0.5

Given the following code using exponential weighted mean (ewm), what is the resulting list of values?

Data Analysis Python

import pandas as pd
s = pd.Series([10, 20, 30, 40])
result = s.ewm(alpha=0.5, adjust=False).mean()
print(result.tolist())

A [10.0, 15.0, 20.0, 25.0]

B [10.0, 20.0, 30.0, 40.0]

C [10.0, 15.0, 25.0, 35.0]

D [10.0, 15.0, 22.5, 31.25]

💡 Hint

Remember that with adjust=False, the ewm mean is calculated recursively using the formula: new_mean = alpha * current_value + (1 - alpha) * previous_mean.

Starting with 10, the next values are calculated as: 15 = 0.5*20 + 0.5*10, 22.5 = 0.5*30 + 0.5*15, 31.25 = 0.5*40 + 0.5*22.5.

🔧 Debug

advanced

Identify the error in expanding window code

What error will this code raise and why?

Data Analysis Python

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

A The output is [nan, nan, nan] because min_periods=4 is greater than the number of elements.

B TypeError because min_periods must be a float, not int.

C ValueError because min_periods cannot be greater than the length of the series.

D The output is [1.0, 1.5, 2.0] ignoring min_periods.

💡 Hint

Check what happens when min_periods is larger than the available data points.

The expanding window requires at least min_periods data points to compute the mean. Since the series has only 3 elements and min_periods=4, all results are NaN.

🚀 Application

advanced

Choosing parameters for ewm to smooth data

You have daily sales data with sudden spikes. You want to smooth the data using ewm with a half-life of 3 days. Which code snippet correctly applies this smoothing?

A s.ewm(halflife=3).mean()

B s.ewm(half_life=3).mean()

C s.ewm(alpha=3).mean()

D s.ewm(span=3).mean()

💡 Hint

Check the exact parameter name for half-life in pandas ewm.

The correct parameter name is 'halflife' (all lowercase, no underscore). Using 'halflife=3' applies exponential smoothing with a half-life of 3 periods.

🧠 Conceptual

expert

Difference between expanding and ewm window functions

Which statement correctly describes the difference between expanding and ewm window functions?

A Both expanding and ewm apply equal weights but differ in window size.

B Expanding windows apply exponentially decreasing weights, while ewm includes all data equally from start to current point.

C Expanding windows include all data from the start to current point equally, while ewm applies exponentially decreasing weights to past data.

D Expanding windows only consider a fixed-size window, while ewm considers all data points.

💡 Hint

Think about how weights are assigned in each method.

Expanding windows calculate statistics using all data points from the start up to the current point with equal weight. Ewm applies weights that decrease exponentially for older data points, giving more importance to recent data.

Practice

1. What does the expanding() window function do in data analysis?

easy

A. Calculates statistics using a fixed-size sliding window

B. Calculates statistics using only the last 3 data points

C. Calculates statistics by giving more weight to recent data points

D. Calculates statistics using all data points up to the current one

Solution

1. Step 1: Understand expanding() function

   The expanding() function includes all data points from the start up to the current point for calculations.

2. Step 2: Compare with other window types

   Unlike rolling windows or ewm, expanding uses all past data, not a fixed window or weighted recent data.

3. Final Answer:

   Calculates statistics using all data points up to the current one -> Option D

4. Quick Check:

   expanding() = all data so far [OK]

Hint: expanding() uses all data up to now, no fixed window [OK]

Common Mistakes:

• Confusing expanding() with rolling() fixed window
• Thinking ewm() is the same as expanding()
• Assuming expanding() only uses recent data

2. Which of the following is the correct syntax to calculate the exponentially weighted mean of a pandas Series data with a span of 3?

easy

A. data.ewm(span=3).mean()

B. data.expanding(span=3).mean()

C. data.rolling(window=3).ewm().mean()

D. data.ewm(window=3).mean()

Solution

1. Step 1: Recall ewm() syntax

   The ewm() function uses parameters like span to control decay; span=3 is valid.

2. Step 2: Check each option

   data.ewm(span=3).mean() uses correct syntax: data.ewm(span=3).mean(). Others misuse parameters or combine methods incorrectly.

3. Final Answer:

   data.ewm(span=3).mean() -> Option A

4. Quick Check:

   ewm(span=3) is correct syntax [OK]

Hint: Use ewm(span=3).mean() for weighted mean with span 3 [OK]

Common Mistakes:

• Using expanding() instead of ewm() for weighted mean
• Passing window parameter to ewm() which is invalid
• Chaining rolling() before ewm() incorrectly

3. Given the pandas Series data = pd.Series([10, 20, 30, 40]), what is the output of data.expanding().mean().tolist()?

medium

A. [10.0, 15.0, 20.0, 25.0]

B. [10.0, 20.0, 30.0, 40.0]

C. [10.0, 15.0, 25.0, 35.0]

D. [10.0, 20.0, 25.0, 30.0]

Solution

1. Step 1: Calculate expanding mean step-by-step

   Expanding mean at each point is average of all values up to that index:
   Index 0: 10 / 1 = 10.0
   Index 1: (10+20)/2 = 15.0
   Index 2: (10+20+30)/3 = 20.0
   Index 3: (10+20+30+40)/4 = 25.0

2. Step 2: Match calculated list with options

   The list is [10.0, 15.0, 20.0, 25.0], which matches [10.0, 15.0, 20.0, 25.0] exactly.

3. Final Answer:

   [10.0, 15.0, 20.0, 25.0] -> Option A

4. Quick Check:

   Expanding mean averages all so far [OK]

Hint: Expanding mean averages all data up to current index [OK]

Common Mistakes:

• Calculating rolling mean instead of expanding mean
• Using last value only instead of average
• Miscomputing cumulative sums

4. You run the code data.ewm(span=2).mean() but get an error. Which fix will solve the problem?

medium

A. Import pandas as pd before using data

B. Replace span with window parameter

C. Use data.ewm(span=2).mean() on a pandas Series, not a list

D. Call mean() before ewm()

Solution

1. Step 1: Identify cause of error

   The ewm() method is a pandas Series method. If data is a plain list, it causes an error.

2. Step 2: Correct usage context

   Convert data to a pandas Series before calling ewm(), e.g., pd.Series(data).ewm(span=2).mean().

3. Final Answer:

   Use data.ewm(span=2).mean() on a pandas Series, not a list -> Option C

4. Quick Check:

   ewm() needs pandas Series [OK]

Hint: ewm() works only on pandas Series, not plain lists [OK]

Common Mistakes:

• Trying to use ewm() on Python lists
• Using wrong parameter names like window in ewm()
• Calling mean() before ewm()

5. You have daily sales data with some missing days. You want to smooth the sales trend giving more weight to recent days but still include all past data. Which pandas window function and parameter combination is best?

hard

A. data.expanding(min_periods=5).mean() to average all data after 5 days

B. data.ewm(span=5, adjust=False).mean() to weight recent days more

C. data.rolling(window=5).mean() to use last 5 days only

D. data.expanding().mean() to average all data equally

Solution

1. Step 1: Understand smoothing with weights

   To give more weight to recent days, ewm() is appropriate because it applies exponential decay.

2. Step 2: Consider missing days and all past data

   ewm() includes all past data but weights recent points more; adjust=False gives a smoother result.

3. Step 3: Compare options

   data.ewm(span=5, adjust=False).mean() to weight recent days more uses ewm(span=5, adjust=False) which fits the requirement best. Others either use equal weights or fixed windows.

4. Final Answer:

   data.ewm(span=5, adjust=False).mean() -> Option B

5. Quick Check:

   ewm() weights recent data more [OK]

Hint: Use ewm(span=5, adjust=False) for weighted smoothing with all past data [OK]

Common Mistakes:

• Using expanding() which weights all data equally
• Using rolling() which ignores older data beyond window
• Not setting adjust=False for smoother ewm