Why time-based analysis reveals trends in Data Analysis Python - Challenge Your Understanding

Challenge - 5 Problems

❓ Predict Output

intermediate

What is the output of this time series rolling mean calculation?

Given a time series data, what is the output of the rolling mean calculation shown below?

Data Analysis Python

import pandas as pd

data = pd.Series([10, 20, 30, 40, 50], index=pd.date_range('2024-01-01', periods=5))
rolling_mean = data.rolling(window=3).mean()
print(rolling_mean.tolist())

A [nan, nan, 20.0, 30.0, 40.0]

B [10.0, 15.0, 20.0, 30.0, 40.0]

C [nan, 15.0, 20.0, 30.0, 40.0]

D [10.0, 20.0, 30.0, 40.0, 50.0]

💡 Hint

Remember, rolling mean with window=3 needs 3 values to compute the first mean.

The rolling mean with window size 3 returns NaN for the first two values because there are not enough data points to calculate the mean. Starting from the third value, it calculates the mean of the current and previous two values.

❓ data_output

intermediate

How many peaks are detected in this time series data?

Using the following time series data, how many peaks are detected by the code?

Data Analysis Python

import numpy as np
from scipy.signal import find_peaks

data = np.array([1, 3, 7, 1, 2, 6, 0, 1])
peaks, _ = find_peaks(data)
print(len(peaks))

A 2

B 1

C 4

D 3

💡 Hint

Peaks are points higher than their neighbors.

The peaks are at indices 2 (value 7), 5 (value 6), and 7 (value 1, which is higher than its left neighbor 0). Total of 3 peaks.

❓ visualization

advanced

Which plot shows a clear upward trend over time?

Given these four plots of time series data, which one clearly shows an upward trend?

Data Analysis Python

import matplotlib.pyplot as plt
import pandas as pd
import numpy as np

dates = pd.date_range('2024-01-01', periods=50)
data1 = pd.Series(np.random.normal(0, 1, 50), index=dates)
data2 = pd.Series(np.linspace(0, 10, 50) + np.random.normal(0, 1, 50), index=dates)
data3 = pd.Series(np.sin(np.linspace(0, 10, 50)), index=dates)
data4 = pd.Series(np.random.normal(5, 1, 50), index=dates)

plt.figure(figsize=(10, 6))
plt.subplot(2, 2, 1)
plt.plot(data1)
plt.title('A')

plt.subplot(2, 2, 2)
plt.plot(data2)
plt.title('B')

plt.subplot(2, 2, 3)
plt.plot(data3)
plt.title('C')

plt.subplot(2, 2, 4)
plt.plot(data4)
plt.title('D')

plt.tight_layout()
plt.show()

A Plot B

B Plot D

C Plot C

D Plot A

💡 Hint

Look for a steady increase in values over time.

Plot B shows a line with a positive slope plus some noise, indicating an upward trend. Others show noise, oscillation, or no clear trend.

🔧 Debug

advanced

What error does this time series resampling code produce?

What error will this code raise when trying to resample a time series?

Data Analysis Python

import pandas as pd

data = pd.Series([1, 2, 3], index=[1, 2, 3])
resampled = data.resample('D').mean()
print(resampled)

A ValueError: Invalid frequency string

B AttributeError: 'Series' object has no attribute 'resample'

C TypeError: Only valid with DatetimeIndex, TimedeltaIndex or PeriodIndex, but got an instance of 'Int64Index'

D No error, prints resampled data

💡 Hint

Check the index type required for resampling.

Resampling requires a time-based index like DatetimeIndex. Here the index is integers, so it raises a TypeError.

🚀 Application

expert

Which method best reveals seasonal trends in monthly sales data?

You have monthly sales data for 5 years. Which method best reveals seasonal trends?

A Calculate daily differences between sales values

B Calculate a 12-month rolling average to smooth data

C Plot histogram of sales values

D Use linear regression on raw monthly sales

💡 Hint

Seasonal trends repeat every year, so smoothing over 12 months helps.

A 12-month rolling average smooths out short-term fluctuations and highlights yearly seasonal patterns. Linear regression fits a trend but misses seasonality. Histogram shows distribution, not time trends. Daily differences are irrelevant for monthly data.

Practice

1. Why is time-based analysis important in data science?

easy

A. It removes all missing data automatically.

B. It helps us see how data changes over time to find trends.

C. It ignores the order of data points.

D. It only works with numbers, not dates.

Solution

1. Step 1: Understand the role of time in data

   Time-based analysis focuses on data points collected over time to observe changes.

2. Step 2: Identify the benefit of time-based analysis

   By analyzing data over time, we can detect trends and patterns that are not visible in static data.

3. Final Answer:

   It helps us see how data changes over time to find trends. -> Option B

4. Quick Check:

   Time-based analysis reveals trends = D [OK]

Hint: Time shows how data evolves; trends need time order [OK]

Common Mistakes:

• Thinking time-based analysis ignores data order
• Believing it only works with numbers, not dates
• Assuming it automatically cleans missing data

2. Which of the following is the correct way to convert a column named 'date' to datetime in pandas?

easy

A. df['date'] = convert_to_date(df['date'])

B. df['date'] = datetime(df['date'])

C. df['date'] = pd.datetime(df['date'])

D. df['date'] = pd.to_datetime(df['date'])

Solution

1. Step 1: Recall pandas datetime conversion function

   pandas uses pd.to_datetime() to convert columns to datetime format.

2. Step 2: Check each option for correctness

   df['date'] = pd.to_datetime(df['date']) uses the correct function and syntax. Options B, C, and D use invalid or non-existent functions.

3. Final Answer:

   df['date'] = pd.to_datetime(df['date']) -> Option D

4. Quick Check:

   Use pd.to_datetime() for date conversion = A [OK]

Hint: Use pd.to_datetime() to convert date columns [OK]

Common Mistakes:

• Using datetime() instead of pd.to_datetime()
• Trying pd.datetime() which does not exist
• Assuming a function named convert_to_date exists

3. Given the following code, what will be the output?

import pandas as pd

data = {'date': ['2023-01-01', '2023-01-02', '2023-01-08'], 'value': [10, 20, 30]}
df = pd.DataFrame(data)
df['date'] = pd.to_datetime(df['date'])
df.set_index('date', inplace=True)
weekly_sum = df.resample('W').sum()
print(weekly_sum)

medium

A. A DataFrame with weekly sums: 2023-01-01 sum=10, 2023-01-02 to 2023-01-08 sum=50

B. A DataFrame with daily sums for each date

C. An error because resample needs a column, not index

D. Empty DataFrame because dates are not sorted

Solution

1. Step 1: Understand resample with weekly frequency

   Resampling with 'W' groups data by week ending on Sunday. 2023-01-01 (Sunday) falls in week ending 2023-01-01, 2023-01-02 (Monday) to 2023-01-08 (Sunday) fall in week ending 2023-01-08.

2. Step 2: Calculate sums per week

   First week sum: 10; second week sum: 20 + 30 = 50.

3. Final Answer:

   A DataFrame with weekly sums: 2023-01-01 sum=10, 2023-01-02 to 2023-01-08 sum=50 -> Option A

4. Quick Check:

   Weekly resample sums values correctly = C [OK]

Hint: Resample groups by time; sum adds values per period [OK]

Common Mistakes:

• Thinking resample works on columns instead of index
• Assuming daily sums instead of weekly
• Believing resample requires sorted dates (pandas sorts automatically)

4. What is wrong with this code snippet for time-based analysis?

import pandas as pd
data = {'date': ['2023-01-01', '2023-01-02'], 'value': [5, 10]}
df = pd.DataFrame(data)
df['date'] = pd.to_datetime(df['date'])
df.set_index('date')
weekly_avg = df.resample('W').mean()
print(weekly_avg)

medium

A. resample('W') cannot be used with mean().

B. pd.to_datetime is used incorrectly.

C. The index is not set inplace, so resample fails on original index.

D. DataFrame is missing a 'value' column.

Solution

1. Step 1: Check index setting

   df.set_index('date') returns a new DataFrame but does not change df unless inplace=True is used or reassigned.

2. Step 2: Understand resample requirement

   Resample works on the datetime index. Since index was not set inplace, df still has default integer index, causing wrong grouping.

3. Final Answer:

   The index is not set inplace, so resample fails on original index. -> Option C

4. Quick Check:

   set_index needs inplace=True or reassignment = A [OK]

Hint: Use inplace=True or assign set_index result [OK]

Common Mistakes:

• Forgetting inplace=True when setting index
• Thinking resample works without datetime index
• Assuming mean() is invalid with resample

5. You have daily sales data for a year. You want to find monthly sales trends but notice some days are missing. Which approach best reveals accurate monthly trends?

hard

A. Convert dates to datetime, set as index, then resample monthly with sum(), filling missing days with 0.

B. Ignore missing days and calculate monthly sum directly on raw data.

C. Convert dates to string and group by month substring, then sum values.

D. Use daily data without conversion and average all values.

Solution

1. Step 1: Prepare data with datetime index

   Convert the date column to datetime and set it as the DataFrame index for time-based operations.

2. Step 2: Resample monthly and handle missing days

   Use resample('M').sum() to aggregate monthly sales. Fill missing days with 0 to avoid undercounting.

3. Step 3: Avoid incorrect grouping methods

   Grouping by string substrings or ignoring missing days can cause inaccurate trends.

4. Final Answer:

   Convert dates to datetime, set as index, then resample monthly with sum(), filling missing days with 0. -> Option A

5. Quick Check:

   Proper datetime index + resample + fill missing = B [OK]

Hint: Set datetime index, resample monthly, fill missing with zero [OK]

Common Mistakes:

• Grouping by string instead of datetime index
• Ignoring missing days causing wrong sums
• Not converting dates to datetime before resampling