Window functions (expanding, ewm) in Data Analysis Python - Mini Project: Build & Apply

Analyzing Daily Sales Trends with Window Functions

📖 Scenario: You work in a small store that tracks daily sales. You want to understand how sales change over time and spot trends. Using window functions like expanding and exponentially weighted moving averages (ewm) helps you see the bigger picture beyond daily ups and downs.

🎯 Goal: Build a simple Python program that uses expanding and ewm window functions on daily sales data to calculate cumulative and smoothed sales values.

📋 What You'll Learn

Create a pandas DataFrame with daily sales data

Add a configuration variable for the smoothing factor

Calculate expanding sum of sales

Calculate exponentially weighted moving average (ewm) of sales

Print the DataFrame with original and calculated columns

💡 Why This Matters

🌍 Real World

Stores and businesses use expanding sums to track total sales over time and ewm to smooth out daily fluctuations for better trend analysis.

💼 Career

Data analysts and scientists use window functions like expanding and ewm to prepare and analyze time series data for reports and decision-making.

1

Create daily sales data

Create a pandas DataFrame called sales_data with two columns: 'day' and 'sales'. Use these exact values: days 1 to 7, and sales values 100, 120, 130, 90, 150, 170, 160.

Data Analysis Python

# Create the sales_data DataFrame with day and sales columns
# Your code here

Hint

Use pd.DataFrame with a dictionary containing the lists for 'day' and 'sales'.

2

Set smoothing factor for ewm

Create a variable called alpha and set it to 0.3. This will be the smoothing factor for the exponentially weighted moving average.

Data Analysis Python

import pandas as pd

sales_data = pd.DataFrame({
    'day': [1, 2, 3, 4, 5, 6, 7],
    'sales': [100, 120, 130, 90, 150, 170, 160]
})

# Create alpha variable for smoothing factor
# Your code here

Hint

Just create a variable named alpha and assign it the value 0.3.

3

Calculate expanding sum and ewm average

Add two new columns to sales_data: 'expanding_sum' which is the expanding sum of sales, and 'ewm_avg' which is the exponentially weighted moving average of sales using the alpha variable.

Data Analysis Python

import pandas as pd

sales_data = pd.DataFrame({
    'day': [1, 2, 3, 4, 5, 6, 7],
    'sales': [100, 120, 130, 90, 150, 170, 160]
})

alpha = 0.3

# Calculate expanding sum and assign to 'expanding_sum'
# Calculate ewm average with alpha and assign to 'ewm_avg'
# Your code here

Hint

Use expanding().sum() on the sales column for cumulative sum.
Use ewm(alpha=alpha).mean() on the sales column for smoothed average.

4

Print the sales data with calculations

Print the sales_data DataFrame to display the original sales, expanding sum, and ewm average columns.

Data Analysis Python

import pandas as pd

sales_data = pd.DataFrame({
    'day': [1, 2, 3, 4, 5, 6, 7],
    'sales': [100, 120, 130, 90, 150, 170, 160]
})

alpha = 0.3

sales_data['expanding_sum'] = sales_data['sales'].expanding().sum()
sales_data['ewm_avg'] = sales_data['sales'].ewm(alpha=alpha).mean()

# Print the sales_data DataFrame
# Your code here

Hint

Use print(sales_data) to show the DataFrame with all columns.

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