To analyze and address the given problem, we will perform the following steps:

Step-by-Step Process

1. Organize Data: Structure the given sales data into a usable format, filling in any missing values if necessary.
2. Plot Raw Data: Create a chart displaying the sales values over the years.
3. 3-Year Moving Average: Compute and plot the 3-year moving average on the same chart.
4. 7-Year Moving Average: Compute and plot the 7-year moving average on the same chart.
5. Comparison: Analyze and describe the differences between the smoothed curves using the two moving averages.

Let me process this data and create the necessary charts. pandas as pd import matplotlib.pyplot as plt

Data from the table (after interpreting and organizing)

data = { "Year": [2004, 2005, 2006, 2007, 2008, 2009, 2010, 2011, 2012, 2013, 2014, 2015, 2016, 2017, 2018, 2019, 2020, 2021, 2022], "Sales": [55, 77, 90, 94, 91, 72, 67, 63, 77, 84, 94, 87, 76, 80, 78, 77, 75, 91, 69] }

Create a DataFrame for easy manipulation

df = pd.DataFrame(data)

Calculate moving averages

df['3-Year Moving Average'] = df['Sales'].rolling(window=3).mean() df['7-Year Moving Average'] = df['Sales'].rolling(window=7).mean()

Plot the raw data and the moving averages

plt.figure(figsize=(14, 8))

Plot raw data

plt.plot(df['Year'], df['Sales'], marker='o', label='Raw Sales Data', color='blue')

Plot 3-year moving average

plt.plot(df['Year'], df['3-Year Moving Average'], label='3-Year Moving Average', color='orange', linestyle='--')

Plot 7-year moving average

plt.plot(df['Year'], df['7-Year Moving Average'], label='7-Year Moving Average', color='green', linestyle='--')

Customize the chart

plt.title("Sales Data with Moving Averages (2004-2022)", fontsize=16) plt.xlabel("Year", fontsize=14) plt.ylabel("Sales (in millions)", fontsize=14) plt.legend(fontsize=12) plt.grid(True) plt.tight_layout()

Show the chart

plt.show()### Chart Explanation

1. Raw Sales Data: The blue line shows fluctuations in the company's sales over the years, with notable peaks and troughs.
2. 3-Year Moving Average: The orange dashed line smooths the data by averaging sales over every 3-year window, reducing short-term fluctuations while preserving general trends.
3. 7-Year Moving Average: The green dashed line provides a more pronounced smoothing by considering a 7-year window. This results in a less sensitive curve, highlighting longer-term trends.

Observations

• 3-Year Moving Average: Captures short-term changes effectively, showing more detailed patterns like smaller peaks and dips.
• 7-Year Moving Average: Highlights broader trends while suppressing noise, ideal for identifying long-term trends.

Would you like detailed calculations or further explanations?

Related Questions

1. How are moving averages calculated, and why are they useful for trend analysis?
2. What happens if we use a larger window (e.g., 10-year moving average)?
3. How do moving averages relate to other smoothing techniques, like exponential smoothing?
4. Can moving averages be used to forecast future sales data?
5. How do short-term fluctuations affect business decision-making compared to long-term trends?

Tip

When analyzing data trends, choose the moving average window size based on your goal: shorter windows for detail, longer windows for a broader perspective.