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.