Moving averages in ML Python

Introduction

Moving averages help smooth out data to see trends better. They reduce noise from random ups and downs.

To understand the general trend of stock prices over time.

To smooth sensor data that has random fluctuations.

To analyze temperature changes over days or months.

To prepare data before feeding it into a machine learning model.

To detect changes or shifts in time series data.

Syntax

ML Python

def moving_average(data, window_size):
    return [sum(data[i:i+window_size]) / window_size for i in range(len(data) - window_size + 1)]

The window_size is how many data points you average at once.

The output list is shorter than the input because the window slides over the data.

Examples

This calculates the average of every 3 numbers in the list.

ML Python

data = [1, 2, 3, 4, 5]
window_size = 3
averages = moving_average(data, window_size)
print(averages)

Here, the moving average uses a window of 2, so it averages pairs of numbers.

ML Python

data = [10, 20, 30, 40, 50, 60]
window_size = 2
averages = moving_average(data, window_size)
print(averages)

Sample Model

This program smooths daily temperature data using a moving average with a window size of 3.

ML Python

def moving_average(data, window_size):
    return [sum(data[i:i+window_size]) / window_size for i in range(len(data) - window_size + 1)]

# Example data: daily temperatures
temperatures = [22, 24, 19, 23, 25, 21, 20]
window = 3
smoothed = moving_average(temperatures, window)
print(f"Original temperatures: {temperatures}")
print(f"Smoothed temperatures with window {window}: {smoothed}")

Important Notes

Choosing a larger window size smooths data more but can hide quick changes.

Moving averages work best with evenly spaced data points.

There are different types like simple, weighted, and exponential moving averages.

Summary

Moving averages help see trends by smoothing data.

They average a fixed number of points called the window size.

Useful for preparing and understanding time series data.

Practice

1. What is the main purpose of using a moving average in data analysis?

easy

A. To smooth out short-term fluctuations and highlight longer-term trends

B. To increase the number of data points in a dataset

C. To remove all noise from the data completely

D. To predict exact future values without error

Solution

1. Step 1: Understand the role of moving averages

   Moving averages smooth data by averaging nearby points, reducing short-term ups and downs.

2. Step 2: Identify the main goal

   The goal is to reveal longer-term trends by reducing noise, not to remove noise completely or predict exact values.

3. Final Answer:

   To smooth out short-term fluctuations and highlight longer-term trends -> Option A

4. Quick Check:

   Moving average = smoothing trends [OK]

Hint: Moving averages smooth data to show trends clearly [OK]

Common Mistakes:

• Thinking moving averages increase data points
• Believing moving averages remove all noise
• Assuming moving averages predict exact future values

2. Which of the following Python code snippets correctly computes a simple moving average with window size 3 for a list data?

easy

A. [data[i] / 3 for i in range(len(data))]

B. [sum(data[i:i+3]) for i in range(len(data)-3)]

C. [sum(data[i:i+3]) / 3 for i in range(len(data)-3)]

D. [(data[i] + data[i+1] + data[i+2]) / 3 for i in range(len(data)-2)]

Solution

1. Step 1: Understand moving average calculation

   A simple moving average with window 3 averages each group of 3 consecutive elements.

2. Step 2: Check each option's correctness

   [(data[i] + data[i+1] + data[i+2]) / 3 for i in range(len(data)-2)] correctly sums three consecutive elements and divides by 3, iterating till len(data)-2.
   [sum(data[i:i+3]) for i in range(len(data)-3)] sums but does not divide by 3.
   [sum(data[i:i+3]) / 3 for i in range(len(data)-3)] divides but uses range(len(data)-3), which is too short.
   [data[i] / 3 for i in range(len(data))] divides single elements by 3, not averaging groups.

3. Final Answer:

   [(data[i] + data[i+1] + data[i+2]) / 3 for i in range(len(data)-2)] -> Option D

4. Quick Check:

   Sum 3 elements / 3, range correct = [(data[i] + data[i+1] + data[i+2]) / 3 for i in range(len(data)-2)] [OK]

Hint: Sum 3 elements and divide by 3, loop till len-2 [OK]

Common Mistakes:

• Forgetting to divide by window size
• Using wrong range length causing index errors
• Averaging single elements instead of groups

3. Given the code below, what is the output?

data = [2, 4, 6, 8, 10]
window = 2
moving_avg = [sum(data[i:i+window]) / window for i in range(len(data) - window + 1)]
print(moving_avg)

medium

A. [2.0, 4.0, 6.0, 8.0, 10.0]

B. [3.0, 5.0, 7.0]

C. [3.0, 5.0, 7.0, 9.0]

D. [6.0, 8.0, 10.0]

Solution

1. Step 1: Calculate moving averages manually

   Window size is 2, so average pairs:
   (2+4)/2=3.0
   (4+6)/2=5.0
   (6+8)/2=7.0
   (8+10)/2=9.0

2. Step 2: Confirm output list length and values

   Length is len(data)-window+1 = 5-2+1=4, matching 4 values above.

3. Final Answer:

   [3.0, 5.0, 7.0, 9.0] -> Option C

4. Quick Check:

   Pairs averaged = [3.0, 5.0, 7.0, 9.0] [OK]

Hint: Average pairs sliding by one, length = len - window + 1 [OK]

Common Mistakes:

• Confusing window size with output length
• Calculating sums but forgetting to divide
• Off-by-one errors in range length

4. The following code is intended to compute a moving average with window size 3, but it misses the last window. What is the problem?

data = [1, 2, 3, 4, 5]
window = 3
moving_avg = [sum(data[i:i+window]) / window for i in range(len(data)-window)]
print(moving_avg)

medium

A. The range should be len(data) - window + 1 to include the last window

B. The window size is too large for the data list

C. sum() cannot be used on list slices

D. Division by window size should be outside the list comprehension

Solution

1. Step 1: Analyze the range length

   Range is len(data)-window = 5-3=2, but to cover all windows it should be len(data)-window+1 = 3.

2. Step 2: Understand impact of incorrect range

   Using len(data)-window misses the last valid window slice, causing incomplete results.

3. Final Answer:

   The range should be len(data) - window + 1 to include the last window -> Option A

4. Quick Check:

   Range length = len - window + 1 [OK]

Hint: Use range(len(data) - window + 1) for full coverage [OK]

Common Mistakes:

• Using len(data) - window instead of +1
• Thinking sum() can't handle slices
• Misplacing division outside comprehension

5. You have daily sales data for 10 days: [10, 12, 11, 14, 13, 15, 16, 14, 13, 12]. You want to smooth this data using a moving average with window size 4 but only want to keep averages where the window's average is greater than 13. Which Python code correctly computes this filtered moving average?

hard

A. [sum(data[i:i+4])/4 for i in range(len(data)-4) if sum(data[i:i+4])/4 > 13]

B. [avg for i in range(len(data)-3) if (avg := sum(data[i:i+4])/4) > 13]

C. [sum(data[i:i+4])/4 for i in range(len(data)-3) if sum(data[i:i+4]) > 13]

D. [sum(data[i:i+4])/4 for i in range(len(data)-3) if sum(data[i:i+4])/4 < 13]

Solution

1. Step 1: Understand window size and range

   Window size 4 means averaging groups of 4 elements, so range is len(data)-3 = 10-3=7.

2. Step 2: Filter averages greater than 13

   [avg for i in range(len(data)-3) if (avg := sum(data[i:i+4])/4) > 13] uses assignment expression to compute average once and filter if > 13.
   [sum(data[i:i+4])/4 for i in range(len(data)-4) if sum(data[i:i+4])/4 > 13] uses wrong range (len(data)-4=6), missing last window.
   [sum(data[i:i+4])/4 for i in range(len(data)-3) if sum(data[i:i+4]) > 13] filters sum > 13, not average > 13.
   [sum(data[i:i+4])/4 for i in range(len(data)-3) if sum(data[i:i+4])/4 < 13] filters averages less than 13, opposite condition.

3. Final Answer:

   [avg for i in range(len(data)-3) if (avg := sum(data[i:i+4])/4) > 13] -> Option B

4. Quick Check:

   Use assignment expression to filter averages > 13 [OK]

Hint: Use assignment expression (walrus) to filter averages [OK]

Common Mistakes:

• Using wrong range length missing last windows
• Filtering sum instead of average
• Using wrong comparison operator